Time value of money; simple and compound interest and discount; real returns; equations of value; loan schedules; valuation of fixed coupon bonds; valuation of real return bonds; term structure of interest rates; no arbitrage pricing; valuation of forward contracts; binomial option valuation. Duration and Immunization
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.
ACTSC 613Statistics for Actuarial Science0.50 units
Discrete and continuous random variables; generating functions; dependence; maximum likelihood estimation, functions of random variables; confidence intervals, hypothesis tests; condition expectation; compound distributions.
Agency theory; investment decisions; long-term financing and cost of capital; principles of taxation; financial reporting; assessment of capital investment projects.
Micro: Supply and demand; utility theory and risk aversion; production choices; competition; Macro: Fiscal and monetary policy; exchange rates; factors affecting inflation, unemployment, exchange rates and economic growth; introductory game theory; introduction to insurance economics.
Multiple state models; premiums and reserves for stat dependent policies, including joint life and last survivor benefits; cashflow projection methods; deterministic, stochastic and stress testing; embedded options; introduction to pension valuation and funding.
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.
ACTSC 625Casualty and Health Insurance Mathematics0.50 units
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.
Risk measures, Binomial and lattice models for option pricing, Black-Scholes option pricing; term structure models. Credit risk; types of models and types of derivatives.
Estimation for lifetime models; estimation for multiple state modes. Graduation. Mortality projection using the Lee Carter model. MLE for Markov multiple state models.
The Actuarial Profession. The Actuarial Control Cycle Impact of Regulation. Consumer needs. Assessing risk. Modeling. Monitoring Experience. Pricing and reserving in life and non-life insurance.
Credibility theory: limited fluctuation; Bayesian; Buhlmann; Buhlmann-Straub; empirical Bayes parameter estimation statistical inference for loss models; maximum likelihood estimation; effect of policy modifications; model selection.
The Mathematics of Survival Models, some examples of parametric survival models. Tabular survival models, estimates from complete and incomplete data samples. Parametric survival models, determining the optimal parameters. Maximum likelihood estimators, derivation and properties. Product limit estimators, Kaplan-Meier and Nelson Aalen. Practical aspects.
Mathematical techniques used to price and hedge derivative securities in modern finance. Modelling, analysis and computations for financial derivative products, including exotic options and swaps in all asset classes. Applications of erivatives in practice.
ACTSC 855Advanced Life Insurance Practice0.50 units
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.
ACTSC 961Mathematical Methods of Loss Reserving0.50 units
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.
This course explores the ways that insurers and regulators in different countries try to monitor and control solvency. In particular we consider the efficacy of different regimes, as well as the effect on product design and pricing. Companies may use different methods to assess their own insolvency risk. We will consider how internal assessment of solvency may differ from the regulator's assessment, and we will look at how insurers try to manage the insolvency risk using asset-liability modelling and financial risk management. Solvency assessment may take a whole company perspective, or may be considered by individual product portfolios and both approaches will be discussed. A substantial element of the course will be a review of some of the recent research in this area. Although the emphasis will be on life insurance, we will also look at the methods and problems associated with non life business.
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.
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.
This course deals with stochastic interest rate models in both discrete time and continuous time. It also covers the theory and practice of instruments such as options, futures, derivative securities and other complex financial instruments.
This course covers topics in the pricing and valuation of derivative securities. It focuses on the underlying theoretical models and examines applications to contemporary finance problems.
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.
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.