Syllabus for
Master of Science (Actuarial Science)
Academic Year  (2021)

MSc Actuarial Science is a multi-disciplinary programme that applies both qualitative and quantitative (Mathematical and Statistical) methods to assess and analyze different risks in financial markets like banking and insurance markets and non-financial markets like manufacturing, trading, government organizations. This course provides a strong foundation in enhancing the core principles and techniques of Actuarial Science and also equips students with adequate skills to analyze and solve real-world actuarial problems.

This course will help students to predict the financial impact of probable future events on a business policy or a financial project initiated by an organization. The process usually involves analysing the data from the past, modelling the future, assessing the risks involved, and communicating what the results mean in financial terms to the senior level management. Students will get a good exposure on market relevant tools and technique used by actuaries from different domains.  

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: Act with integrity in a difficult situation by complying with professional ethics.

PO6: Demonstrate proficiency in various insurance products and services and assume the role of insurance advisors

PO7: 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

PO8: Demonstrate leadership traits, communication skills and innovative thinking for optimal performance in personal, professional, societal and environmental domains.

PO9: Evaluate personal and professional choices in terms of ethical values and governance and their application to society, business and professions

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 stresses importance of professional ethics which is important for actuarial profession. Discuss some case studies and scenarios to strengthen the understanding of scenarios that we may encounter in actuarial profession. The business awareness touches on specific areas to understand a business environment better and related actuarial functions.

What is Professional Ethics - It's importance to any profession – How related to Actuarial professional and why actuarial bodies focus seriously on these aspects

Your professional responsibilities - Possible Dilemma's in an actuarial role - Discuss on how as an actuary we will be able to handle them - Discuss four scenarios from different actuarial capacities and understand the importance of handling dilemma's better.

Understanding a business environment – How to financial companies create value to customers- - Financial Service industry (any one country) - External and Internal factors impacting financial environment - Strategic thinking in business - Relevant legal principles (any one country)

Different functions in an Insurance/Reinsurance company – Actuarial predominate functions (ex: Pricing, Valuation, Risk management etc) – Purpose of different actuarial functions – Roles and responsibilities of actuaries in actuarial functions.

2. Insurance Business Environment & Insurance Company Operations – K.C. Mishra

3. IFOA website on professional dilemma videos as base for discussion

2. The Insurance Management playbook

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: