Syllabus for
Master of Science (Actuarial Science)
Academic Year  (2015)

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%

Christ University understands the limitations of compartmentalized knowledge which is not adequate enough to face the challenges of the globalized world. With a mission to prepare the students for life and not just for the acquisition of a degree, it encourages every initiative that would help students make perfect connections with the world outside. Inspired by the educational philosophy of Rousseau, Emerson, Ivan Illich, Paulo Freire, Gandhi, Tagore and Blessed Chavara, the University formulated this concept of Holistic Education more than fifteen years ago and included it in the curriculum and makes necessary changes every year. A group of teachers drawn from across the streams go through the whole process of designing the curriculum through a series of intense discussions under the broad classification of three skills: personal, interpersonal and societal. 

I Semester UG

Personal Skill : Goal Setting and  Cyber Etiquettes

Inter-Personal Skill : Dealing with Competition and Leading and Following

Societal Skill : Gender Sensitization and Community Living

III Semester UG

Personal Skill : Spirituality and Transition to Adulthood

Inter-Personal Skill : Alienation and Blocks in Relationship

Societal Skill : Gender Stereotypes and Good Governance

I Semester PG 

Personal Skill : Accountability and Mindful Living

Inter-Personal Skill : Alienationand Blocks in Relationship

Societal Skill : Gender Sensitization and Sustainable Development

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance. The aim of the Financial Mathematics course is to provide grounding in Financial Mathematics and their applications. 

Time value of money - Simple interest, compound interest, depreciation, investing over a period. Cash flow models – Zero coupon bonds, fixed interest securities, index linked securities, equity, annuity, an interest on loan, repayment loan, examples of cash flow scenarios. Interest rates - Nominal rate, effective rate and force of interest. 

Immediate and due Annuities - 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.

Equation of value and the yield, project appraisals – net present value, internal rate of return, comparing projects, non-annual rates of interest, term annuities.

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

The aim of the Probability and Mathematical Statistics subject is to provide grounding in the aspects of Statistics and in particular Statistical modeling that are of relevance to actuarial work.

Importance of statistics, population and a sample, quantitative and qualitative data, collection of primary and secondary data, questionnaire design. Measurement scales-nominal, ordinal, interval and ratio. Presentation of numerical data in tables and graphs – stem and leaf display, frequency distribution, frequency curves, histogram. Presentation of categorical data in tables and charts – Bar and pie charts, Pareto diagram, contingency tables. Measures of central tendency – mean, median, mode, geometric mean, deciles, quartiles percentiles. Measures of dispersion – range, inter-quartile range, standard deviation, and coefficient of variation. Box plot, skewness and kurtosis.

Definition ,concepts and components of Time Series, estimation of trend by moving average  and method of least squares, Seasonal variation and its computation.

Random experiment, sample space and event. Classical, and empirical definition of probability. Addition rule and multiplication rule of probability. Conditional probability and Bayes theorem. Random variable- discrete and continuous. Distribution function. Probability mass and density functions. Expectation variance and moments. Conditional expectation and conditional variance. Distributions of functions of a random variable. ( one and two dimension)

Discrete distributions - Uniform, Bernoulli, binominal, geometric, negative binomial, hyper geometric and Poisson distributions. Mean, variance and moment and cumulant generating function, properties of distributions. Continuous distributions -Uniform, Exponential, Gamma, Beta Normal distribution. Mean, variance and moment generating function, properties of distributions.

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

The Master of Science in Actuarial Science program is designed to prepare students to pursue careers in quantitative finance.  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.

Loan schedule - Flat rate, annual effective rate, loan repayment schedules with payment of equal capital components or payment of equal installments with varying interest and capital components. Investments - fixed interest government borrowings, tax, security, debentures and unsecured loan stocks, money-weighted and time-weighted rates of return and linked internal rate of interest on investment or a fund.

Compound interest problems in various forms of Actuarial applications, government securities, other fixed interest securities, real rates of interest, calculating yields, equities, properties, real-estate, commodities, and numismatics. 

Discrete time, par yield, yield to maturity, spot rates and forward rates, continuous spot rates, duration and convexity of a cash flow sequence and their use in Redington’s immunization of portfolio of liabilities.

Fixed interest rate models and variable interest rate models with independent distributions for successive periods, arbitrage pricing and derivatives, forward and future contracts, their pricing.

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

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. Some areas of corporate finance that are covered in electives - leasing, mergers and acquisitions, working capital management - will be omitted or covered in less detail than they merit. Course 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. 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, financial institutions.

This course will make the students understand the areas of risk management, techniques available to handle the same and focus on insurance as a risk management tool for individuals and corporate.

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 - 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. Processes, structure, prospecting, sales, proposal renewals, channels of distribution. Lapse and surrenders and its impact on insurance business, adverse selection, renewal of policies. IRDA guidelines on investment of premium.

Settlement options in a life insurance contract - maturity claims and death claims. Introduction to group life insurance - definition of a group, types of groups, determination of benefit levels, eligibility requirements, termination of provisions. Reinsurance – Reinsurance, importance of insurance and types of reinsurance.

This course introduces the student to both micro and macro concepts and gives an overview to the subject of Economics.

Meaning, nature & scope of Managerial Economics; Importance of Managerial Economics; Basic concepts – wants, goods, production & resources, Scarcity and choice, Opportunity cost, Utility, Value, Price, wealth, income, yield, profit, savings, Time value of Money.

Demand (Determinants, Demand function) - Law of Demand – Variations in demand, Supply (Determinants, Supply function) – Law of Supply –Variations in Supply, Market equilibrium and changes in equilibrium (reference to product markets & factor markets), Time time dimension of market adjustment, dealing with uncertainty & risk.Market failure – meaning & types - Public goods – Externalities - Merit goods - Demerit goods. Elasticity of Demand – Price elasticity of demand – factors determining elasticity of demand – its measurement and its application in business decisions, concepts of Income, Cross - Promotional elasticity of demand. Elasticity of Supply – factors determining elasticity of supply.

Production Analysis: Production – Firm and Industry – Production function – Short run & long run – Law of variable proportions - Returns to scale (increasing, constant and decreasing returns to scale) – Economies of scale and Diseconomies of scale. Cost - Cost concepts (Absolute cost and opportunity cost, Accounting cost and Economic cost) – Fixed and Variable cost – TC, AC & MC, Cost-output relationship in the short run - Cost-output relationship in the long run. Revenue – TR, AR & MR - Revenue with no change in price – Revenue with change in price.   Market Structure: Features of perfect competition and monopoly – Concept of price discrimination – Features of Monopolistic competition & Oligopoly – Price indeterminateness – Cartel formation - Different forms of price leadership – Game theory. Regulation – Competition policy - Scope of regulation

Macroeconomy – meaning, measuring the size of the economy - National income – methods of national income estimation - Business use of national income data - Understanding national income: the circular flow model & its components. Macroeconomic analysis - Aggregate Demand & Aggregate Supply Framework. Monetary system: Meaning & functions of money, Money multiplier, supply of money, demand for money, equilibrium in the money market, effect of a change in the money supply Macroeconomic problems – Business Cycles/ Unemployment & Inflation, Philips Curve Macroeconomic policies – Demand side & Supply side policies, Fiscal policy & Monetary policy. International trade, balance of payments and exchange rates.

2.      Stockman,  Introduction to Macroeconomics.

3.      William H Branson,  Macroeconomic Theory and Policy.  

Application of statistical methods used for a description of analysis of business problems. The development of analytic skills is enhanced by use of one of the widely available statistical packages and graphing calculation.

 Scatter plots for bivariate data, calculation of correlation coefficient using, Karl Pearson’s and Spearman’s rank correlation coefficient, simple linear regression, concepts of statistic, parameter, pivotal quantity, sampling distribution and standard error. Chi square, t and F distributions.

Concepts of point estimation, properties of estimators, unbiasedness, efficiency, consistency and sufficient condition for consistency. Sufficiency, factorisation theorem, Rao-Cramer lower bound of variance and related results. Minimum variance bound estimator, likelihood function. Methods of estimation-maximum likelihood and method of moments.

Concepts of confidence interval and confidence coefficient, confidence interval for mean, difference between means, variance and ratio of variances under normality. Large sample confidence interval for proportions and correlation coefficients.

Statistical hypotheses-Simple and composite. Errors of Type I and Type II, size and power of a test, Statistical tests, Critical region.  Test for the mean, equality of two means, variance and equality of two variances (large and small samples), large sample tests for proportions, test for simple correlation coefficients-simple. Test for regression coefficient. Chi – square test - Test for goodness of fit, test for independence of attributes. Most Powerful (MP), Uniformly Most Powerful (UMP) tests, Neyman Pearson Lemma, Monotone Likelihood Ratio Property.

The Financial Economics includes courses covering the working of the financial markets for bonds, stocks, currencies and derivatives (futures and forwards, options and swaps), the asset pricing models and valuation principles. Behavioral finance and stochastic dominance concepts are covered. Also stochastic calculus and Brownian motion will be applied extensively in arriving at derivative valuation formulae. 

Introduction to financial economics, economic models, economic vs statistical models, General modeling principles, Efficient market hypothesis (EMH), Three forms of EMH, Active vs Passive Investment Strategies, over reactions, under reactions, anomalies,  utility theory – consumer choice and preferences, the expected utility theorem, certainty equivalence, risk seeking and risk averse investor, Measuring risk aversion, the log utility function and power utility function, Limitations of utility theory, Stochastic dominance, first order and second order stochastic dominance, relationship between dominance concepts and utility theory. Behavioral finance – anchoring, prospect theory, framing, myopic loss aversion, estimating probabilities,  over confidence, mental accounting and the effect of options.

Measures of Investment risk- variance, semi variance, shortfall probabilities, Value at Risk (VaR), Tail VaR, modern portfolio theory – Mean variance portfolio theory, opportunity set, efficient frontier, benefits of diversification.

Models of asset returns – multifactor models, macro-economic models, fundamental factor models, statistical factor models. Asset pricing models – CAPM, the separation theorem, Capital Market line (CML), Security Market Line (SML), Beta, zero beta model, arbitrage pricing theory

Product differentiation,integrals for simple integrands, properties of the integral, integrals for general integrands, Brownian motion – properties, standard and geometric Brownian motion, non-differentiability of sample paths, martingales – discrete and continuous,  stochastic calculus and Ito processes, Ito process for random numbers, stochastic differential equations, Diffusion and Ito process, The Ornstein Uhlenbeck process. 

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. Some areas of corporate finance that are covered in electives - leasing, mergers and acquisitions, working capital management - will be omitted or covered in less detail than they merit. 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. Term sources - Medium term and short term sourcesof Finance for an organization. medium term sources - hire purchase, credit sale, leasing, bank loans. Short term sources - bank overdraft, trade credit, factoring, bill of exchange, commercial paper.

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, Share buyback.

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, Modigliani and Miller’s two propositions of irrelevance Capital Asset Pricing Models.

Cost of capital for the company, cost of capital for a project,NPV, IRR, Payback Period, Discounted Payback Period, evaluation of risky projects, risk analysis and dealing with risks, risk matrices, Stochastic modeling, risk mitigation.

Stephen A. Ross, Bradford D. Jordan and Randolph Westerfield, Essentials of Corporate Finance. McGraw-hill, 2010.

The aim of the course is to enable the students to understand the various types of general insurance policies that are available in the market, the range of coverage in each type of policy, the clauses used and how the rates and premium are determined.

Requirements of non-life insurance contract, framework of general insurance in India, organization and working of general insurance companies, financial management of general insurance companies and their investments, capital management and planning and reporting requirements.    

Liability insurance, Property insurance, Financial loss insurance and fixed benefits insurance - Understanding the various products under each category and the risks attached. Fire insurance contracts - requirements, how a fire insurance contract works, understanding the cover note and various other aspects of fire insurance, consequential loss policy, underwriting factors. Marine insurance - understanding the various types of marine contracts like single voyage policy, multiple voyage policy etc, the working of marine insurance contract, underwriting factors, challenges for the marine insurance segment. Motor vehicle insurance - Underwriting factors, coverage under the policy, rating parameters, no-claim bonus and its relevance, other related factors. Health insurance and Annuity products - a brief introduction to these products. Future innovation of general insurance products in India: Analysis of General Insurance products in the developed nations and studying the potential of those products being introduced in Indian markets.

Steps involved in product design and development, general insurance pricing, claims management in general insurance, challenges in claims management, role of reinsurance in general insurance and analysis of the financial statements of insurance companies. . Technology impact on General insurance product distribution - understanding the new distribution channels and impact of the technology on the product design, pricing and claim settlement.

Role of the regulator, capital management of general insurance companies: Basel II norms, guidelines regarding the investment of premium, laws governing insurance management and accounting, asset liability management of general insurance companies and liability valuation, investment strategies of general insurance companies, the fundamental legal principles and taxation aspects of general insurance companies and analysis of the financial statements of insurance companies.

The aim of Actuarial modeling is to study advanced non-life insurance mathematics, individual risk models, collective risk models, ruin models, Actuarial reserve models: Bonus-malus system, IBNR techniques and generalized linear models in Actuarial Science.

Principles of Actuarial modeling, binomial and Poisson Models, generalization of the model, maximizing the likelihood, the actuarial estimate, strengths and weakness of the binomial model and Poisson model, estimating the underlying force of mortality.

Stochastic Processes - Definition, types, stationary process, weakly stationary process. Exposed to risk - principle of correspondence, exact calculation of initial exposed to risk and central exposed to risk., censoring in mortality investigation, its various types and illustrations.

Markov property, filtration, Poisson process. Markov Chains - Basic features, Chapman-Kolmogorov equations, time-homogeneous and time-inhomogeneous Markov chains, model for no claim discount policy, simple random walk, a model for accident proneness, stationary probability distribution, irreducibility, modeling using Markov Chains.

Assumptions, analysis, a simple two decrement model, time-homogeneous Markov jump processes, structure Markov jump processes, time-inhomogeneous Markov jump processes, applications to mortality and morbidity models.

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

The aim of this subject is to instil the students ability to apply, in simple situations, the mathematical and economic techniques and the principles of actuarial planning and control needed for the operation on sound financial lines of providers of pensions or other employee benefits.

Nature of the gratuity liability, funding for it, advantages of the scheme, installation and administration of the scheme, methods of funding- individual and cash accumulation and life cover- OYRGTA - one year renewable group term assurance- under the gratuity scheme.

Need for pension, funding for it, advantages of a pension scheme, pension options, installation and operation of pension schemes and funding under cash accumulation system and the deferred annuity system, defined benefit scheme and the defined contribution scheme, group Leave Encashment Scheme, group annuity scheme for privately managed superannuation funds and schemes providing index-linked pension, group schemes for employer’s vrs, group savings-linked scheme- GSLI - nature of the scheme, extent of cover, minimum membership, conditions for entry into the scheme, contributions, administration of the scheme and the employer’s obligations, National pension scheme and its ramifications, PFRDA and regulatory aspects.

Its basis, free-cover limit, insurability conditions and the OYRGTA premium rating for employer-employee groups, non-employer employee groups and GSLI schemes, premium calculation for different group schemes, experience rating - its rationale and methods, transfer of master policies and funds- transfer of equitable interest from one scheme to another, transfer of annuitants from one group to another.

Purpose, data and methods of valuation for different schemes,consistency checks for valuation data, surplus and declaration of bonus-simple reversionary and group pension terminal bonus and submission of D returns, mortality investigation under group schemes and procedure for taking over the investments of the privately managed gratuity and superannuation trust funds and reinsurance for group schemes, AS 15 and IFRS aspects.

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

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.

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.

Premiums, frequency of payment, the net premium definition, notation, the insurer’s loss random variables, provisions, prospective provision, retrospective provision, conditions for equality of prospective and retrospective provisions, provision conventions, net premium provisions, whole life policies, continuous functions, non-annual premiums, term assurances, other contracts, recursive calculation  of  provisions, conditions for recursive calculations, net premium provisions at successive durations, the equations of equilibrium for a whole life assurance, mortality profit dead stain at risk, expected death strain, actual death strain.

Variable payments, whole life assurance, term assurance, whole life annuity payable annually in arrears and advance, temporary annuities, with-profit contracts, types of bonus, calculating net premiums and net premium provisions for with-profit contracts, net future loss random variables, gross premiums and provisions for fixed and variables benefit contract.

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

The aim of this course is to provide a further grounding in mathematical and statistical techniques of particular relevance to financial work.

Optimum strategies under the theory of games, decision function and a risk function, apply decision criteria to determine which decision functions are best with respect to a specified criterion, minimax criterion and the Bayes criterion.

Properties of the statistical distributions which are suitable for modelling individual and aggregate losses, moments and moment generating functions of loss distributions including the gamma, exponential, Pareto, generalised Pareto, normal, lognormal, Weibull and Burr distributions, statistical inference to select suitable loss distributions for sets of claims, concepts of excesses (deductibles) and retention limits, operation of simple forms of proportional and excess of loss reinsurance, distribution and corresponding moments of the claim amounts paid by the insurer and the reinsurer in the presence of excesses (deductibles) and reinsurance, to estimate the parameters of a failure time or loss distribution when the data is complete or when it is incomplete, using maximum likelihood and the method of moments.

Models appropriate for short term insurance contracts in terms of the numbers of claims and the amounts of individual claims, major simplifying assumptions underlying the models, moment generating function of the sum of N independent random variables; in particular when N has a binomial, Poisson, geometric or negative binomial distribution, compound Poisson distribution and sum of independent random variables each having a compound Poisson distribution also has a compound Poisson distribution, mean, variance and coefficient of skewness for compound binomial, compound Poisson and compound negative binomial random variables, moment generating functions and moments of aggregate claims over a given time period for the models. 

Concept and general properties of stationary, I(0), and integrated, I(1), univariate time series, stationary random series, concept of a filter applied to a stationary random series, backwards shift operator, backwards difference operator and the roots of the characteristic equation of time series, concepts and basic properties of autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) time series, discrete random walks and random walks with normally distributed increments, both with and without drift, multivariate autoregressive model, cointegrated time series, univariate time series models have the Markov property and describe how to rearrange a univariate time series model as a multivariate Markov model, outline the processes of identification, estimation and diagnosis of a time series, the criteria for choosing between models and the diagnostic tests, non-stationary, non-linear time series models, deterministic forecasts from time series data, using simple extrapolation and moving average models, applying smoothing techniques and seasonal adjustment when appropriate. 

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

The Financial Economics includes courses covering the working of the markets for bonds, stocks, currencies and derivatives (futures and forwards, options and swaps), as well as microeconomics, advanced macroeconomics and econometrics.

Growth and profitability, constraints on growth alternative, growth strategies, internal growth, external growth through merger, external growth through strategic  alliance, a transaction cost approach, globalization, government intervention in markets, the objectives of government intervention, types of market failure, types of Government intervention, the case for less Government intervention.

Government intervention in market, government and the firm, competition policy, policies towards research and development, supply-side policy, problems on supply-side policy, industrial policy. International trade - trading patterns, advantages of trade, arguments for restricting trade, balance of payments, exchange rates, the world trading system and the WTO. 

Macroeconomics environment - macroeconomics objectives, the circular flow of income, measurements of national income, determination national income, economics growth, unemployment, inflation, demand side macroeconomics policy, fiscal policy, monetary policy, demand management general, current demand side policy in the UK.

Interest rates - functions and meaning of money, financial system, supply of money, demand for money, equilibrium in the money market, effect of a change in the money supply, interest rate models. Business activity, unemployment and inflation: unemployment and inflation, the disappearance of the Phillips curve and business cycles.

Steven E. Shreve, Stochastic calculus for Finance II: continuous – time model. Springer 2010. 

This course develops the basic actuarial techniques that are used in later work. Topics covered include simple annuities and assurance, profit testing, competing risk, pension funds and mortality.

This subject will train the students and enhance them to compete and excel in the Institute of Actuaries exam.

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.

Profit testing - determining premium and provisions using profit testing, profit criterion, linked policy using cash flow techniques ,Zeroising negative and  effect of pricing used provisioning bases on a profit test, valuing  benefits that are contingent upon competing risk, multiple state approach, multiple decrement tables, deriving department probabilities from transition intensities, deriving the independent probabilities from the dependent probabilities, multiple decrement tables, premium conversion relationships and profit testing.

Salary scale, salary related pension benefits and contributions, age retirement benefits, III health retirement benefits , death in  service benefits, scheme contributions, expected cash flows generated by pension and contributions, classifications of benefits, determining expected cash flows, expected amount payable, probability of payments, expected cash flows using commutation functions to value salary related benefits and contributions, death benefits, members contributions, benefits and options available to an individual leaving a pension scheme, return of contribution, a referred pension, immediate pension and transfer of cash equivalent.

Standardization, principal factors contributing to variation in mortality and morbidity, occupation , nutrition, housing , climate and geographical location, education, genetics, selection - temporary initial selection, class selection time selection, adverse selection, spurious selection, selection in life assurance and  pensions business, life assurance, pension funds, crude mortality rate, AS15 and IFRS.

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.

This course will enable students to develop a good understanding of the fundamentals of Health Insurance, structuring of products, management of underwriting & claims, various stakeholders involved in the business, regulatoryaspects and the role of Governmental agencies and will also enable students to develop a good understanding of the approach, considerations and implementation aspects of Enterprise Risk Management, with a strong appreciation of ‘real life’ constraints and issues.

This subject will train the students and enhance them to compete and excel in the Institute of Actuaries exam.

Concept of holistic approach / enterprise view, traditional Risk Management vs ERM, benefits of ERM, impact on corporate risk culture, framework for ERM, ERM as a part of corporate governance, risk: vision, mission & strategies, risk appetite & tolerance, risk management policies, communication & awareness, risk management organization / roles & responsibilities, ERM models & regulations - COSO & ISO frameworks, solvency II and regulatory implications.

Risk categories / risk classification, identification / prioritization of risks, understanding cause & implication of risks, related risks / co-relation between risks, aggregation of risks and its impact, risk assessment & quantification, practical Issues related to assessment, various approaches to risk control & mitigation, risk financing: approach and options. ERM projects -design and implementation, issues and problems with implementation, KPIs, monitoring and measurement of effectiveness, technology support for ERM.

Healthcare – Public / Private services, stakeholders in healthcare services, healthcare financing – Public/Private, role of Government & public agencies, insurance as a healthcare financing tool, products and coverage, indemnity products (individual & group), critical Illness Plans, long term care plans, travel insurance plans / International covers, micro-insurance, high deducible / floater / benefit plans, distribution of health insurance - channels of distribution, issues related to selling/ mis-selling.

Risk classification & assessment, pricing considerations, underwriting considerations & practices, adverse selection / pre-existing conditions, group underwriting, proposal/ policy forms, standard clauses & terms, tailor-made policies. Claims Management - Standard Claims Process, cashless procedure, claim reserving, fraud management in claims, customer services / customer grievance management, importance of coding (icd-10) and data management, regulations related to health insurance, health insurance in markets outside India (US, UK).

1.      Kenneth Black and Harold D. Skipper, Life and HealthInsurance. Prentice Hall.

2.      Insurance Institute of India, IC 27: Health Insurance, Insurance Institute of India, 2010.

3.      Sim Segal, Corporate Value of Enterprise Risk Management:The next step in business management, Wiley, 2011.

This course provides students with a practical understanding of the various software tools used by actuaries in practice and equips them with the necessary skills to solve actuarial related issues with Excel, VBA programming and SQL programming. Students will learn how to apply these skills through hands - on exercises and projects.

This subject will train the students and enhance them to compete and excel in the Institute of Actuaries exam.

Understanding of data, real-life data, data cleaning, meaning, need and methodology. Life insurance - fitting of mortality curves, graduation applications, estimation of CDF of lifespan, plotting observed data and confidence limits, preparing columns of life table, calculation of gross premium, net premium, profit testing, joint life applications, calculating unit prices, unit movements and simple embedded values.General Insurance - scatter plot for loss data, fitting of loss distribution, distribution for aggregate losses, ruin probability, pricing, experience rating, reserving and GLM.

Calculating expected liability for employee benefits such as gratuity, leave encashment, pension (defined benefit), disclosures under accounting standards, reconciliation and experience adjustments, funding requirement, expectedpension based on defined contribution and calculating profits of annuity products, expected losses payable on a healthcare policy for different kinds of loss events, aggregate benefits payable on healthcare policies, pricing of health policies using burning cost model floater principles, calculating Beta from one year’s period for share prices, CAPM, calculating volatility, computing option prices using binomial model and Black-Scholes model, accounting disclosures using ESOP guidance note and interest rate model applications. 

Calculation of discounted payback period, IRR and NPV, solving simple and compound interest rate problems, demonstrating a comprehension of scenario and stress tests, analysis of sensitivity, evaluating effects of internal and external factors on discount rates.

Introduction of VBA macros, VBA sub-procedure, VBA functions, create VBA macros, record actions to create them, write VBA code functions and VBA examples.

1.      Edward W. Frees, Regression Modeling with actuarial and Financial Applications. Cambridge University Press, 2009.

2.       Stuart A. Khugman, Harry H. Panjer and Gordan E. Willmot,Loss Models: From Data to Decisions. Wiley-Interscience, 2008.

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

2.      J. Bagajewicz, Philip Booth and Robert Chadburn, Modern Actuarial Theory and Practice. Crc press, 2004.

The aim of this paper is to introduce some key elements of research methodology to first time research students.

This subject will train the students and enhance them to compete and excel in the Institute of Actuaries exam.

Meaning of research, significance of research, the research process, types of research, research objectives, research approaches, research hypotheses, criteria of good research, characteristics, research in an evolutionary perspective, defining the research problem.

Research design, definition, types of research design, exploratory and causal research design, descriptive and experimental design, different types of experimental design, validity of findings, internal and external validity, variables in research, measurement and scaling, different scales, construction of instrument, validity and reliability of instrument.

Types of data, primary vs secondary data, methods of primary data collection, survey vs observation, experiments, construction of questionnaire and instrument, validation of questionnaire, sampling plan, sample size, determinants optimal sample size, sampling techniques, probability vs non–probability sampling methods, data preparation, editing, coding, data entry, validity of data, qualitative vs quantitative data analyses, bivariate and multivariate statistical techniques, factor analysis, discriminant analysis, cluster analysis, multiple regression and correlation, multidimensional scaling, application of statistical software for data analysis.

Research report, different types, contents of report, need of executive summary, chapterization, contents of chapter, report writing, the role of audience, readability, comprehension, tone, final proof, report format, title of the report, ethics in research, ethical behaviour of research, subjectivity and objectivity in research.

1.      Uma Sekaran, Research methods for Business. Wiley India, 2006.

2.      Donald R. Cooper and Pamela S. Schindler, Business Research methods. Tata Mc Graw Hill, 2006.

1.      Alan Bryman and Emma Bell, Business Research methods. Oxford
University Press, 2008.

2.      O. R. Krishnaswami, Methodology of Research in Social Sciences. Himalaya Publishing, 2010.

Advanced non-life insurance mathematics. Individual risk models, collective risk models, ruin models. Actuarial reserve models: Bonus-malus system, IBNR techniques. Generalized linear models in Actuarial Science. 

This subject will train the students and enhance them to compete and excel in the Institute of Actuaries exam.

Distribution of future lifetime, force of mortality, rates of mortality, expectations of life, Gompertz’s law and Makeham’s law, estimating the lifetime distribution function using the Kaplan-Meier and Nelson-Aalen models.

Parametric models for the hazard function, covariates, form of Cox model. proportional hazard model, estimating regression parameters, partial likelihood, hypothesis testing, Balducci’s assumption, generalized model, actuarial estimate, strengths and weaknesses.

Introduction, graduation of observed mortality rates, the underlying assumptions, comparison with other tables, standard tables graduation, the need for graduation, reasons for graduation, the theoretical argument, the practical Argument , features of a graduation, smooth graduation, testing the smoothness of a graduation, problems on Chi- Square test, standardized deviations test, signs test cumulative deviations, grouping of sign test, serial corrections tests.

Graduation by Parametric Formula, the graduation process, graphical graduation, the graphical graduation process, comparison of different methods, graduation by parametric formula, graduation by reference to a standard table, Statistical tests of a graduation, testing a graduation and effect of duplicate policies.

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

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

1.       Zdzislaw Brzezniak and Tomasz Zastawniak, Basic stochastic processes: A course through exercises. Springer, 2000.

2.      Grimmett Geoffery and David Stizaker, Probability and random processes. Oxford University press, 2001.

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