Syllabus for
Master of Science (Actuarial Science)
Academic Year  (2023)

M Sc Actuarial Science is designed to give candidates from quantitative, commerce and Economic backgrounds an opportunity to launch their careers in Actuarial Science. It is a discipline that applies Mathematical and Statistical methods to assess risk in the insurance and financial industries. This course provides a solid foundation in the core principles and techniques of Actuarial Science. MSc Actuarial Science is a two-year postgraduate course spread over four semesters comprising modules on Financial Mathematics, Actuarial Statistics, Insurance and Economics. The course covers key areas in global business with in-depth coverage of Risk Management opening a plethora of opportunities in the insurance and global investment sectors. The course is dedicated towards dealing with real-world scenarios and application of the analytical process that students are trained for; practical application, case studies and market analysis with experts guiding individuals will be an important aspect of the learning process. A qualified person in MSc actuarial science would be having a basic foundation and a solid platform from which they can proceed to becoming an actuary. They can use their quantitative skills to analyze data from the past and present, in order to predict the future and help others make prudent and intelligent financial decisions.

Programme Outcome/Programme Learning Goals/Programme Learning Outcome:

PO2: Demonstrate expertise in Mathematics and Statistics to perform Actuarial modeling to formulate solutions for problems concerning the industry

PO3: Exhibit proficiency in the areas of finance and economics and assume the role of actuarial experts and offer pertinent consultancy services

PO4: Exhibit expertise in enterprise risk management and thereby equip organisations to manage risks effectively

PO5: Apply advanced knowledge of research and statistics to conduct independent research investigations and formulate solutions to complex problems of insurance and actuarial science by applying right tools.

PO6: Demonstrate leadership traits, communication skills and innovative thinking for optimal performance in personal, professional, societal and environmental domains.

The applicable evaluations are CIA-1, CIA –2 (based on Mid-Sem examination), and CIA –3 based on internals.

Pattern of End Semester Examination question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered.  

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance. The aim of this course is to provide grounding in Financial Mathematics and their applications. Increasingly firms of all types, but especially financial institutions, investment banks, and commodities firms, rely upon highly sophisticated mathematical models to identify, measure, and manage risk.Topics covered also include the life table, life assurance contracts, life annuity contracts.

Aims of data analysis, The data analysis process, Data Sources and Reproducible research, Principles of actuarial modeling from the new course material- Models, Modeling-the benefits and limitations, Stochastic and deterministic models, Discrete and continuous state spaces and time sets, Scenario-based and proxy models, Suitability of a model, Short term and long term properties of a model, Analysis the output of a model, Sensitivity testing and Communication of the results. Cashflow process, Example sof cashflow scenarios, Insurance contracts – Pure endowment, Endowment assurance, term assurance, Contingent annuity, Car insurance policy, Health cash plan

Interest - Simple interest, compound interest, Accumulations factors, Principle of consistency, Present Values, Discount Rates, Effective rates of interest and discount, Equivalent Rates, Nominal Rates of Interest and Discount, Accumulating and discounting using nominal rate of interest and discount, The force of Interest, Accumulating and discounting using force of interest, Relationships between effective, nominal and force of interest, Force of interest as a function of time, Definition of real and money rate of interest, Usefulness of real and money interest rates, Present values of cashflows, Discrete and continuous cashflows, Valuing cashflows, Constant interest rates, Payment stream, Sudden changes in interest rates.

Present values and future values of an annuity - payments made in arrear, payment made in advance, perpetuities. Discounting and accumulation - Present value and accumulated value of a stream of payments using specified interest rates, net present value and deferred annuities. Increasing annuity immediate, increasing annuity due, decreasing annuity immediate, decreasing annuity due, annuity relationships, continuously payable annuity, continuously varying annuities - continuously increasing annuity and continuously decreasing annuity.

Constructing a life table, using the life table, the pattern of human mortality, life table functions at non-integer ages, method 1 - uniform distribution of deaths (UDD), methods 2 - constant force of mortality (CFM), the general patterns of mortality, mortality characteristics, the shape of qx, lx, dx, using the life table to evaluate means and variances, evaluating means and variances without use of the life table, select mortality, displaying select rates, constructing select and ultimate life tables, using tabulated select life table functions, evaluating means and variances using select mortality.Life assurance contracts - pricing of life insurance contracts, equations of value, allowance for investment income, present value random variables, expected present value, variance of the present value random variables for life assurance contracts, life assurance benefits payable immediately on death, claim acceleration approximation. Life annuity contracts - annuity due, temporary annuity, temporary annuity due, deferred annuities, deferred annuities due, continuous annuities and evaluation of assurance and annuities.

2. Steven Roman, Introduction to the Mathematics of Finance: From risk management to options pricing. Springer, 2004.

2. David C. M. Dickson, Mary R. Hardy, Howard R. Waters, Actuarial Mathematics for life contingent risk. Cambridge University Press, 2009.

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The aim of this course is to provide grounding knowledge in the aspects of Statistics and Statistical modeling that are of relevance to actuarial work.

Definition and important characteristics of discrete and continuous distributions- Discrete: geometric, binomial, negative binomial, hypergeometric, Poisson, and uniform on a finite set. Continuous: normal, lognormal, exponential, gamma, chi-square, t, F, beta and uniform on an interval. Poisson Process. Generate basic discrete and continuous random variables using the inverse transform method. R Programming. Definition and derivation of moment generating function of random variables, cumulant generating function and probability generating function of discrete, integer-valued random variables; generating moments and cumulants of random variables, by expansion as a series or by differentiation as appropriate

Jointly distributed random variables, marginal and conditional distributions; probability functions of marginal and conditional distributions; expected value of a function of two jointly distributed random variables; covariance and correlation; probability function of sum of two independent random variables as the convolution of two functions; mean and variance of linear combination of random variables; conditional expectations.

Central limit theorem for independent, identically distributed random variables and its applications. Population, sample, parameter and statistic, random sample, sampling distributions of a statistics; sampling distribution of sample mean, sample variance in terms of the population mean, variance and sample size; sampling distribution of t-statistics, F-statistic, and Chi-square statistic and their statistical properties and applications.

Concepts of estimator, estimate; method of moments and method of maximum likelihood estimation for constructing estimators of population parameters; Properties of best estimator: unbiasedness, consistency, efficiency and mean square error; asymptotic distribution of maximum likelihood estimators; concept of confidence interval, construction of confidence intervals for an unknown parameter using sampling distributions, mean and variance of normal distribution, binomial probability and Poisson mean, two-sample situations involving the normal distribution and binomial and Poisson distributions using normal approximation.

2. J. E. Freund, Mathematical Statistics. New Delhi, Prentice hall, 7th ed. 2004.

2. Hogg et al. Introduction to Mathematical Statistics, Pearson Education, 6th ed. 2005. (reprint 2009)

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The course focuses on financial decision making in the modern corporation. An introduction to accounting and interpretation of the accounting information is covered here. Core concepts are integrated into the standard theories of risk and return, valuation of assets and market structure.

Introduction to accounts, accounting standards, basic accounting concepts, contents of annual report, director’s report, auditor’s report, international financial reporting standards, credit, debit, asset, liability, income, expense profit and loss account, balance sheet and cash flow statement.

Construct profit and loss account, balance sheet and cash flow statement.

Depreciation - concept, methods of calculation. Reserves - types and uses.

Holding company, subsidiary company, minority holding, consolidated balance sheet. Understanding how goodwill arises on consolidation. Preparation of Insurance company accounts - technical and non-technical account, profit and loss accounts and balance sheet

Interpretation of accounts using accounting ratios, Accounting ratios to assess security of loan capital and their interpretation. Accounting ratios to enable shareholder analysis and their interpretation, limitations of accounts and Introduction to working capital management.           

2. Atrill, P and McLaney, E, 2015, Management Accounting for decision makers, 8th ed, Pearson

3. Berry, A and Jarvis, R, 2011, Accounting in a business context, 5th ed, Cengage

4. Sloman, J, Garratt, D, Guest, J and Jones, E, 2016, Economics for Business, 7th ed, Pearson

5. Leiwy, D and Perks, R, 2013, Accounting Understanding and Practice, 4th ed, McGraw-Hill

2. The Association of Chartered Certified Accountants, London, 2010, ‘Sustainability reporting matters. What are national governments doing about it?’.  Available at: http://www.accaglobal.com/content/dam/acca/global/PDF-technical/sustainability- reporting/tech-tp-srm.pdf

3. Companies Act, 2006, Contents of the strategic report. Available at: http://www.legislation.gov.uk/ukpga/2006/46/contents

4. FRC: The UK Corporate Governance Code, April 2016

5. The International Integrated Reporting Council, how to prepare an integrated report.  Available at: http://integratedreporting.org/. 

Evaluation Pattern

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

This course will make the students understand the domains of life insurance and pensions, develop an understanding of the different areas of risk management, techniques available to handle the same and focus on insurance as a risk management tool for individuals and corporates.  By virtue of this understanding, it also instills in students the ability to apply the principles of actuarial planning and control needed for the efficient functioning of providers of insurance products.

Introduction and Overview - Definition of risk and categories of risks, insurable risks, types of insurance, risk management and objectives. Key insurance concepts - Concept and role of insurance, fundamental principles, indemnity, insurable interest, subrogation, utmost good faith, contract conditions. Differences between life and non-life contracts, need for regulation and the role of the regulator in the insurance business, professionals in the insurance business-need for professionalism, intermediaries in the insurance contract. IRDA regulations on Actuaries, Financial planning - Needs analysis, life cycle planning, asset allocation and taxation.

Introduction to Life insurance contracts - Contract conditions and requirements. Types of life insurance products - term life insurance, whole life insurance, endowment policies, unit linked insurance plans and other related products. Riders to a life insurance policy - waiver of premium riders, disability benefit riders, accelerated benefit riders, how a rider works and the advantages of riders. Life insurance policy provisions - incontestability provision, grace period provision, reinstatement provision, operation of free look-in period etc. Life insurance policy beneficiaries - naming a beneficiary, change of beneficiary and related concepts. Factors determining the calculation of premium - understanding mortality. Life insurance underwriting: Life insurance underwriting - Need for risk classification and grouping of risks, agents' role in underwriting, underwriting policy, process of underwriting and restrictions on post-selection underwriting. Documents and premium - Underwriting and actuarial framework. Methods of funding life insurance - Life insurance reserves. Channels of distribution, lapse and surrenders and its impact on insurance business. Reinsurance- need for reinsurance, types of reinsurance, treaty and facultative, proportionate and non-proportionate reinsurance.

Different types of group insurance schemes. Group term Insurance: Group OYRTA Plans, Employers Deposit Linked Insurance Scheme (EDLI), mortgage cover, graded cover, etc. Different types of groups and their characteristics from insurance point of view, benefits provided, group underwriting for employer-employee and other groups, premium rating, Expected claims cost, premium calculation for different group schemes, experience rating-its rationale and methods, prospective and retrospective rating. Group term products- UPR and IBNR Reserve, calculation of UPR and IBNR reserves for Group term policies. Social insurance programs in India.

Need for pension,  role of government in providing pensions, Employee Provident Fund, Employee Pension Scheme 1995, occupational pension schemes, individual personal pension plans, installation and operation of employer run pension schemes, defined  contribution and defined pension plans, associated risks to employer and employees,, insurer administer and self-administered pension schemes, exempt superannuation scheme,  income tax act and rules,  investment norms for self-administered pension schemes, insurer administered pension schemes, National Pensions Scheme, PFRDA and its regulatory aspects. Payment of gratuity act, installation and administration of a gratuity scheme, nature of gratuity liability, exempt gratuity scheme, income tax act and rules, insurance company administered and self-administered gratuity schemes, investment norms for self-administered gratuity schemes, insurer administered gratuity schemes- unit linked, variable insurance plans.

1. Kenneth Black and Harold D. Skipper, Life and Health Insurance. Pearson Education publication, 1999.

2. Emmett. J. Vaughan and Therese Vaughan, Fundamentals of risk and insurance. Wiley publications, 2011.

2. Principles of Insurance :  A publication of the Insurance Institute of India.

3. IC 83: A publication of the Insurance Institute of India.

4. Practice of Life Insurance : A publication of the Insurance Institute of India

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

This course revisits and strengthens the understanding of economics concepts and modules and the theories that underline the subject. It will also give a practical outlook of a subject with reflecting the real-life examples within the academic learning keeping main focus on Micro Economics as topic.

Economic concepts and systems - The classification of economic systems , The command (or planned or centrally controlled/planned) economy , Assessment of the command economy, The free market economy, Assessment of the free-market economy, The mixed economy. 

Main strands of economic thinking - the classical approach – Marxist socialism – the neoclassical approach – Keynesian schools of thought – the monetarist approach – the new classical approach – the Austrian school 

The relationship between demand and price, The demand curve, Other determinants of demand, Movements along and shifts in the demand curve, price elasticity of demand, price elasticity of supply, income elasticity of demand, cross-price elasticity of demand, Equilibrium in market

Total and marginal utility, The one-commodity model: – Optimum consumption – Marginal utility and the demand curve – Weaknesses of the model 

The multi-commodity model: – Optimum combination of goods consumed – Marginal utility and the demand curve

Short-run and long-run changes in production, The law of diminishing returns, The short-run production function: total physical product, The short-run production function: average and marginal product

Perfect Competition, Monopoly, Monopolistic, Oligopoly, Characteristics ,  Barriers to entry ,The importance of costless exit , Assessment of the theory, Contestable markets and the public interest, Cost-based pricing , Variations in the mark-up, Limit pricing, Social efficiency, Externalities, Public good, Market power, Forms of government intervention

Main macroeconomic variables that governments seek to control. Determination of the price level in the economy, Interaction between aggregate supply and aggregate demand in a simple AD-AS model, GDP and its calculation, Circular flow of Income

2. Principles of Macroeconomics – N Gregory

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

This course provides an introduction to the R programming language for data analytics. Students will learn how to use R to import, manipulate, analyze, and visualize data for business applications. The course will cover both basic and advanced topics in R, including data structures, programming, data analysis, and visualization. The course will also introduce students to popular R packages for data analytics, such as dplyr, ggplot2, and tidyr.

Overview of R and its applications in business analytics. Understanding the R interface and basic data structures. Importing and cleaning data in R

Introducing dplyr package for data manipulation. Filtering, summarizing, and transforming data using dplyr

the ggplot2 package for data visualization. Creating basic and advanced visualizations using ggplot2. Customizing visualizations using ggplot2.common statistical models for business analytics. Building and evaluating regression models using R. Performing hypothesis testing using R

R packages for business analytics, such as tidyr, caret, and lubridate. Practical applications of R in business analytics, including time series analysis, predictive modeling, and data mining

2.     R for Data Science" by Hadley Wickham and Garrett Grolemund - 1st Edition, 2017

2.     R Graphics" by Paul Murrell - 2nd Edition, 2021

Evaluation Pattern

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·       Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·       A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·       In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

This course provides a comprehensive introduction to business application software, including tools such as Microsoft Excel, Word, and PowerPoint. Students will learn how to use these tools to efficiently manage data, create professional documents and presentations, and automate common tasks. The course will also cover advanced features in Excel, including data analysis, macros, and pivot tables.

• Overview of Excel and its applications in business
• Understanding the Excel interface and basic formulas
• Data management and manipulation

·       Data analysis using Excel functions such as VLOOKUP, INDEX, and MATCH

·       Macros and VBA programming in Excel

·       Pivot tables and charts

• Overview of Word and its applications in business
• Understanding the Word interface and basic formatting
• Document creation and collaboration

·       Overview of PowerPoint and its applications in business

·       Understanding the PowerPoint interface and basic formatting

Presentation creation and design

2.       Amit Johri, Business Application Software, Himalayan Publishing House 2012

Department of Professional Studies follows a rigorous system of continuous evaluation, and the assessment events include quizzes, tests, assignments, mid-term and end-term exams, individual/group project work, presentations etc.  

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·       Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·       A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·       In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance. The aim of this course is to provide grounding in Financial Mathematics and their applications. Increasingly firms of all types, but especially financial institutions, investment banks, and commodities firms, rely upon highly sophisticated mathematical models to identify, measure, and manage risk.Topics covered also include the life table, life assurance contracts, life annuity contracts.

The equation of value and the yield on a transaction and uncertain payment or receipt, Loan Schedules - Calculating the capital outstanding, Calculating the interest and capital elements, The loan schedule, Instalments payable more frequently than annually and Consumer credit, APR and Flat rate of interest.Bonds, Equity and property- Fixed interest securities, Uncertain income securities, Real rates of interest, The effects of Inflation, Index-linked bonds.

Estimating cashflows, Accumulates value, Net Present value, Internal rate of return, Fixed interest rates, Different interest rates for lending and borrowing, Payback periods,  and Other considerations, Discrete time rates- Discrete time forward rates, discrete time spot rates, Continuous time rates – continuous-time spot rates, continuous time forward rates, Instantaneous forward rates, Theories of term structure of interest rates – Expectation theory, Liquidity preference, Market segmentation, Par yield, Duration, convexity and Immunisation, Redington’s conditions

Evaluating assurance benefits, Evaluating annuity benefits, Premium conversion formulae, continuous annuities and evaluation of assurance and annuities, Expected present values of annuities payable m times each year and Expected present values under a constant force of mortality, Variable payments, Payments varying at a constant compound rate, Payments varying by a constant monetary amount and Conventional with profit contracts.

The gross premium, Gross future loss random variable, Principle of equivalence and Calculating gross premiums using simple criteria other than the equivalence principle, Why hold reserves, Prospective reserves, retrospective reserves, Equality of prospective and retrospective reserves, Recursive relationship between reserves for annual premium contracts and Net premium reserves for conventional without profit contracts.

2. Stephen G. Kellison, The theory of interest. Irwin Mc Graw Hill, 2008.

1. Newton L. Bowers, Actuarial Mathematics. The society of Actuaries, 1986.

2. David C. M. Dickson, Mary R. Hardy, Howard R. Waters, Actuarial Mathematics for life contingent risk. Cambridge University Press, 2009.

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The aim of this course is to provide deeper understanding of higher level statistical inference, and introduce the concepts of Bayesian statistics, Generalized Linear Models and Credibility Theory.

Concept of hypothesis, simple and composite hypothesis; null and alternative hypothesis; type1 and type II errors, test statistic, likelihood ratio, critical region, level of significance, probability value, and power of a test. Basic tests for one and two-sample situations involving normal, binomial, and Poisson distributions and paired data. Chi-square test for goodness of fit, single variance, and independence of two classification criteria. Define and calculate Pearson’s, Spearman’s and Kendall’s measures of correlation for bivariate data, explain their interpretation and perform statistical inference as appropriate

Regression analysis: response and exploratory variables, simple regression model (with single explanatory variable), least square estimates of simple regression model and their significance; multiple linear regression model (with several explanatory variables).

Generalised linear models: Exponential families; Link functions and linear predictors; Deviance of model fitting, the saturated model, scaled deviance, Likelihood ratio test, Residuals analysis and assessment of model fit - Goodness-of-fit tests. Bayesian Statistics: Bayes’ Theorem, Prior and posterior distributions, Loss Functions

Credibility Theory: Credibility- The credibility premium formula; credibility factor, Bayesian credibility, The Poisson/gamma model, the normal/normal model Empirical Bayes credibility theory: Model 1, Model 2.  

2. S. C. Gupta and V. K. Kapoor, Fundamentals of Mathematical Statistics. New Delhi, Sultan Chand and sons, 11th ed. 2002. (reprint 2011)

2. Hogg et al. Introduction to Mathematical Statistics, Pearson Education, 6th ed. 2005. (reprint 2009)

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The course focuses on financial decision making in the modern corporation. The basic issues include: capital budgeting/corporate investment, capital structure, corporate sources of funding, dividend policy and corporate contingent claims, international finance, and financial risk management. Alternate sources of finance to be covered. Course concepts are integrated into the standard theories of risk and return, valuation of assets and market structure.

 The key principles of finance, role of directors and managers, agency theory, company ownership, sole trader, partnership firm, limited company (private and public), and limited liability partnership in UK.

Sources - Long term and short term sources of Finance for an organization.This includes traditional sources such as share capital and loan financing as well as alternate sources of finance such as shadow banking and crowd funding.

Taxation - personal taxation, company taxation, capital gains tax, other taxes, double taxation relief.

Financial instruments - debenture stocks, unsecured loan stocks, eurobonds, preference shares, ordinary shares, convertible unsecured loan stocks, convertible preference shares, warrants, floating-rate notes, subordinated debt, options issued by companies, capital structure and dividend policy

Methods of obtaining a quotation - Introduction, offer for sale, offer for sale by tender, offer for subscription, placing, right issue, scrip issue. Derivatives - forward contracts, future contracts, options and swaps, their characteristics and uses for hedging, weighted average cost of capital

Cost of capital for the company, cost of capital for a project, NPV, IRR, Payback Period, Discounted Payback Period, evaluation of risky projects, understanding the various types of financial risks in capital budgeting, risk analysis and dealing with risks, risk matrices, Stochastic modelling, risk mitigation strategies        

2. Atrill, P and McLaney, E, 2015, Management Accounting for decision makers, 8th ed, Pearson

3. Berry, A and Jarvis, R, 2011, Accounting in a business context, 5th ed, Cengage

4. Leiwy, D and Perks, R, 2013, Accounting Understanding and Practice, 4th ed, McGraw-Hill

5. Sloman, J, Garratt, D, Guest, J and Jones, E, 2016, Economics for Business, 7th ed, Pearson

2. The Association of Chartered Certified Accountants, London, 2010, ‘Sustainability reporting matters. What are national governments doing about it?’.  Available at: http://www.accaglobal.com/content/dam/acca/global/PDF-technical/sustainability- reporting/tech-tp-srm.pdf

3. The International Integrated Reporting Council, How to prepare an integrated report.  Available at: http://integratedreporting.org/. 

4. FRC: The UK Corporate Governance Code, April 2016

5. Companies Act, 2006, Contents of the strategic report. Available at: http://www.legislation.gov.uk/ukpga/2006/46/contents

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The aim of risk modelling is to study mortality models and understanding calculations pertaining to risk exposure. Various mortality models are discussed here. The course also focuses on understanding the stochastic processes and its relevance to modelling.

Stochastic Processes - Definition, types, stationary process, and weakly stationary process, Understanding deterministic and stochastic models.

Markov Property, Markov chains, model for no claim discount policy, stationary distributions, irreducible markov chains and periodic markov chains, modelling using markov chains and checking the goodness of fit for a markov process.

Understanding the two state model and extending the concept to multiple state model, use of Poisson model in understanding mortality estimation. In this chapter we consider a formulation of the problem in which we analyse the random process by which a life passes from one state (alive) to another (dead).  The results are consistent with those that we obtain when we model a person’s future lifetime as a continuous random variable.

State the essential features of a Markov process model.  Define a Poisson process, derive the distribution of the number of events in a given time interval, derive the distribution of inter-event times, and apply these results. 3Derive the Kolmogorov equations for a Markov process with time independent and time/age dependent transition intensities. Solve the Kolmogorov equations in simple cases.  Describe simple survival models, sickness models and marriage models in terms of Markov processes and describe other simple applications. Derive maximum likelihood estimators for transition intensities. Describe an observational plan in respect of a finite number of individuals observed during a finite period of time, and define the resulting statistics, including the waiting times.

Understanding the various assumptions in developing models, UDD, CFM and Balducci assumptions, extending the life time distributions, GompertzMakeham model and humped hazard models and other relevant areas.

1. Question papers from www.actuariesindia.org

2. Fsa Dick London, Survival Models and their estimation. Actex, 1997.

3. Newton L. Bowers, Actuarial Mathematics. The society of Actuaries, 1986.

1. Question papers and examiner’s report from Institute and faculty of actuaries, UK

2. ZdzislawBrzezniak and Tomasz Zastawniak, Basic stochastic processes: A course through exercises. Springer, 2000.

3. J. Medhi, Stochastic Processes, John Wiley, 1994.

4. GrimmettGeoffery and David Stizaker, Probability and random processes. Oxford University press, 2001

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance. The aim of this course is to provide grounding in Financial Mathematics and their applications. Increasingly firms of all types, but especially financial institutions, investment banks, and commodities firms, rely upon highly sophisticated mathematical models to identify, measure, and manage risk.Topics covered also include the life table, life assurance contracts, life annuity contracts.

Creation of financial models in excel, projection of cashflows of various financial assets using excel, solve for the price to be paid for financial assets, Preparation of loan schedules using excel and hence calculate the interest paid and capital outstanding for every future years, performing NPV, IRR and discounted payback period calculations in excel, solving project appraisal problems using excel.

Projecting the cashflows from various life insurance products like whole life insurance, unit linked insurance etc in excel, Calculating the gross/net premium reserves at the start of every year for different type of life insurance products, solve for the premiums of life insurance products using excel, projection of cashflows and hence performing profit testing of life insurance policies

2. Stephen G. Kellison, The theory of interest. Irwin Mc Graw Hill, 2008.

2. Principles of Financial Modelling: Model Design and Best Practices Using Excel and VBA Book by Matthew Rees.

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

3. Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The aim of this course is to provide knowledge of practical application of statistical concepts using R

Discrete and continuous distributions; Central Limit Theorem; Sampling

Estimation theory; Confidence intervals; Hypothesis testing; Data Analysis; Linear Regression

Bayesian statistics; Generalized Linear Models; Credibility Theory and EBCT models

2. J. E. Freund, Mathematical Statistics. New Delhi, Prentice hall, 7th ed. 2004

2. Hogg et al. Introduction to Mathematical Statistics, Pearson Education, 6th ed. 2005. (reprint 2009)

Students are evaluated for each course on the basis of written examination and continuous internal assessments.

·       A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·       In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

This course is designed to provide students with a deep understanding of the concepts and techniques of Risk Modelling and Survival Analysis using R programming. The course focuses on the theoretical and practical aspects of survival analysis, including data visualization, exploratory data analysis, parametric and non-parametric models, time-dependent covariates, and censoring. The course emphasizes hands-on experience through practical sessions, case studies, and projects.

Survival analysis and its application in actuarial science Types of censoring in survival analysis Survival function and hazard function Kaplan-Meier estimator for survival analysis. 

Exponential, Weibull, and Gompertz distributions Maximum likelihood estimation Goodness of fit tests

Cox proportional hazards model Nelson-Aalen estimator Gray's test for comparing cumulative incidence 

Time-varying covariates, Cox model with time-dependent covariates, Marginal structural Cox mode

Types of censoring, Handling censoring in R, Inverse probability weighting

Students are evaluated for each course on the basis of written examination and continuous internal assessments.

·       A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·       In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below:

Continuous Internal Assessment (CIA):

The course shall be subject to CIA and will be in the same pattern as approved by the University in respect of other PG Courses. The applicable evaluations are CIA-1 (based on Mid-Sem examination), CIA –2 and CIA –3 based on internals.

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance and insurance domain. This course develops the basic actuarial techniques that are used in later work. Topics covered include the life table, life assurance contracts, life annuity contracts, net premium, provisions, variable benefits and with – profit polices, profit testing, competing risk, pension funds and mortality.

Random variables to describe join life functions, joint lifetime variables and function, last survivor lifetime random variables, determining simple probabilities involving two lives, evaluating probabilities of death or survival of either or both of two lives, evaluating last survivor functions, determining present values involving two lives, present values of joint life and last survivor assurances and annuities, contingent and reversionary benefits, contingent probabilities of death, present  values of contingent assurances and reversionary annuities, present values of functions with specified terms, expected present values of last survivor assurances, annuities and reversionary annuities that depend upon terms.

Mortality profit on a single policy, Mortality profit on a portfolio of policies, Allowing for death benefits payable immediately, Allowing for survival benefits, Allowing for different premium or annuity payment frequencies and Calculation of mortality profit for policies involving two lives, Health Insurance contracts, multiple state models, Multiple decrement models, Multiple decrement tables and Using multiple decrement tables to evaluate expected present values of cashflows  

Unit linked contracts, Unit funds and non-unit funds, Accumulating with profit contracts, Unitised accumulating with-profit contracts, Charges and benefits under UWP, Evaluating expected cashflows for various contract types – conventional whole life assurance, conventional endowment assurance, Unit-linked endowment assurance, Single premium unitized with-profit contracts, Profit test for annual premium contracts

Summary measures of profit, Profit Vector, Profit Signature, Profit Margin, Net Present Value (NPV), Internal Rate of Return (IRR), Profit testing using the present value random variable, Pricing using a profit test, Pricing and reserving bases, Calculating reserves for unit linked contracts, Incorporating non-unit reserves into the profit test, Calculating reserves for conventional contracts using a profit test, Effect of pricing and reserving bases on a profit test, Setting out the calculation.

1. Stephen G. Kellison, The theory of interest. Irwin Mc Graw Hill, 2008.

2. Alistair Neill, Life Contingencies. Butterworth-heinemann, 1977. 

1. Newton L. Bowers, Actuarial Mathematics. The society of Actuaries, 1986.

2. David C. M. Dickson, Mary R. Hardy, Howard R. Waters, Actuarial Mathematics for life contingent risk. Cambridge University Press, 2009.

Students are evaluated for each course on the basis of written examination and continuous internal assessments. Each paper carries maximum of 100 marks and is evaluated as follows:

·         Written Examinations consists of:

§  Mid Semester Exam – 50 Marks (2 hours duration)

§  End Semester Exam – 100 Marks (3 hours duration)

·         A student should secure a minimum of 50% Marks in the ESE to pass in that paper.

·         In aggregate for each paper, for internal and end semester put together, at least 40 Marks out of 100 must be secured to pass in that paper.

1. Examinations, Question Paper Pattern and Pass Mark/Grade.

For all semesters there shall be a Mid Semester Examination (MSE) for 50 marks per subject and an End Semester Examination (ESE) for 100 marks per subject.

Pattern of question paper for 100 marks of 3 hours’ duration will be as follows:

There will be six questions, each carrying twenty marks, out of which any five has to be answered. 

Minimum marks required for passing ESE shall be as under:

SEMESTER I to IV: 40% per paper Aggregate Average 50%

2. Grading Pattern:

Grading pattern will be the same as approved by the University for PG Courses as detailed herein below: