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.

Principles of financial accounting; construction and analysis of accounts. Sustainability reporting. Financial planning; capital budgeting, assessment of capital projects; long term financing; short term finance and planning

Mean-Variance portfolio theory; utility based portfolio theory; Capital-Asset Pricing Method, Arbitrage Pricing Theory, Efficient Markets Hypotheses; Capital structure and dividend policy; introduction to options with applications in corporate finance. Behavioural finance.

Generalized linear models: multiple linear regression and normal linear model; exponential family; link functions; linear predicators; estimation; testing. Time series: Univariate ARIMA; multivariate AR; ARCH and other non-linear models.

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 models, insurance pricing using generalized linear models, classification and tree-based methods.

This course combines enterprise and quantitative risk management to provide a comprehensive coverage of risk management science with applications in finance, insurance and corporate governance. Topics covered include: risk taxonomy; risk measures; extreme value theory; copulas; stress and scenario testing; interest rate risk management, credit risk management; regulation, including Basel, Basel 3 and Solvency 2; risk adjusted return; capital allocation.

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 is designed to develop students' oral and written communication skills, using examples from actuarial risk management. It includes elements of writing, and also reading and summarizing leading edge work in actuarial theory and practice. Presentations and collaborative work are used to develop essential communication skills in both academic and professional contexts.

Macro methods of runoff analysis: chain-ladder, least squares, separation, payment per claim incurred. Stochastic methods: Reid's method, see-saw, payment per unit of risk, autoregressive models, Kalman filter.

The analysis of the development over time of the surplus on a portfolio of insurance business is considered. The classical Poisson and Sparre Andersen risk models are studied. Unified treatment of moments and distributions of quantities related to the event of ruin is done through a discounted penalty function approach. Random variables of interest include the time of ruin itself, the deficit immediately after ruin occurs, and the surplus immediately prior to ruin. Defective renewal equations and Laplace transforms are utilized extensively. Prerequisites are familiarity with aggregate loss models at the level of ActSc 431/831 or equivalent.

Ruin Theory for heavy-tailed distributions. Fluctuation of maxima and upper order statistics. Extreme value distributions: Weibull, Frechet, Gumbel and generalized Pareto. Mean excess function. Statistical methods for external events. Estimation of parameters of extreme value and excess distributions. Applications in finance and insurance.

The course introduces options and other derivative securities in different asset classes. The main focus is on methods of pricing in a multi-period setting, but continuous-time models are also discussed. Topics may include no-arbitrage pricing theory, the fundamental theory of asset pricing, complete and incomplete markets,and pricing of complex financial instruments.

The course will cover selected and advanced topics in quantitative finance and risk management, with a particular focus on current developments. Topics may include robust and Bayesian portfolio optimization, limits to arbitrage, derivatives pricing under model uncertainty, credit risk models, and models of systematic risk.

The focus of this course is on the statistical modelling, estimation and inference and forecasting of nonlinear financial time series, with a special emphasis on volatility and correlation of asset prices and returns. Topics to be covered normally include: review on distribution and dynamic behaviour of financial time series, univariate and multivariate GARCH processes, long-memory time-series processes, stochastic volatility models, modelling of extreme values, copulas, realized volatility and correlation modelling for ultra high frequency data and continuous time models.