Course subject: Actuarial Science (ACTSC)

Models for future lifetime; insurance and annuity functions; life tables and their use; future loss random variable for a contract; calculations of premiums and reserves; standard international actuarial notation.

Agency theory; investment decisions; long-term financing and cost of capital; principles of taxation; financial reporting; assessment of capital investment projects.

Mean-Variance portfolio theory; Capital-Asset Pricing Method, Arbitrage Pricing Theory, Efficient Markets Hypotheses; Capital structure and dividend policy.

Generalized linear models: multiple linear regression and normal linear model; exponential family; link functions; linear predicators; estimation; testing. Time series: Univariate ARIMA; multivariate AR; applications to economic series.

Frequency and severity models; compound distributions, calculation of moments and probabilities using recursion; Bayesian estimation and credibility; claims reserving for non-life insurance using run-off triangle methods, introductory ruin theory.

This course provides a comprehensive treatment of various techniques from statistics, predictive analytics and machine learning that can be used to analyze data sets relevant for actuarial applications. Specific topics covered include: modeling principles and practice, analysis and estimation of survival and multiple-state models, insurance pricing using generalized linear models, classification and tree-based methods, and Monte Carlo simulation of time series.

Enterprise Risk management. Pricing and valuation. Economic and regulatory capital. Solvency. Investment management.

This course introduces enterprise risk management, with a focus on quantitative analysis and economic capital. Risk classification is first discussed with an emphasis on the types of risk most suited to quantitative methods. Risk measures, such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE or TVaR), are then introduced, and their use by firms and regulators to determine risk capital requirements is further highlighted. Different approaches are considered for developing loss distributions, including frequency/severity analysis and extreme value theory. Copulas and economic scenario generators are used to aggregate dependent risks. Different strategies for mitigating or transferring risk are reviewed. Additional topics that may be covered include credit risk, capital allocation and regulation of financial institutions.

Cash flow projection methods for pricing, reserving and profit testing, deterministic, stochastic and stress testing; pricing and risk management of embedded options in insurance products; mortality and maturity guarantees for equity-linked life insurance.

This course presents advanced mathematical and computational tools useful to study loss frequency and severity models, and also aggregate claims models. Analytic and recursive evaluation of compound distributions are discussed, as well as generalized linear models for frequency and severity models. Other topics covered include pricing and insurance risk processes.

Fundamental concepts in quantitative risk management. Topics typically include: risk measures, extreme value theory, multivariate distributions and copulas. This course has a focus on mathematical and statistical techniques. Other topics may be covered at the discretion of the instructor.

Mixed Poisson and nonhomogeneous birth processes for claim counts; analytic, recursive, asymptotic and approximate evaluation of compound distributions for aggregate claims; reliability concepts and analysis of stop-loss moments; applications for inflation, incurred but not reported claims, and infinite server queues. Prerequisites are familiarity with aggregate loss models at the level of ActSc 431/831 or equivalent.

The course discusses methods and tools for modeling of financial derivatives in the continuous-time setting. Both theory and practical applications are discussed. The first part covers methods of pricing and hedging of derivatives under different assumptions about the dynamics of the underlying economic factors. Topics normally include currency derivatives, American and exotic options, futures contracts, stochastic volatility models and mean-variance hedging. The second part deals with modeling and pricing of interest-rate products. Topics may include short interest rate models, the Heath-Jarrow-Morton Framework, and Libor and swap market models.

Basic optimization: quadratic minimization subject to leanear equality constraints. Effecient portfolios: the efficient frontier, the capital market line, Sharpe ratios and threshold returns. Practical portfolio optimization: short sales restrictions target portfolios, transactions costs. Quadratic programming theory. Special purpose quadratic programming algorithms for portfolio optimization: today's large investment firms expect to solve problems with at least 1000 assets, transactions costs and various side constraints in just a few minutes of computation time. This requires very specialized QP algorithms. An overview of such algorithms will be presented with computational results from commercial problems. The efficient frontier, the capital market line, Sharpe ratios and threshold returns in practice.