Concepts of probability; random variables; combinatorial probability; discrete and continuous distributions; joint distributions, expected values; moment generating functions; law of large numbers and central limit theorems.
Fall 2021, Winter 2022, Summer 2022
Distribution of sample mean and sample variance; t, chi-squared and F distributions; summarizing data by statistics and graphs; estimation theory for single samples: sufficiency, efficiency, consistency, method of moments, maximum likelihood; hypothesis testing: likelihood ratio test; confidence intervals.
Fall 2022, Winter 2023
Linear and multiple regression, analysis of residuals, transformations, variable and model selection including stepwise regression, and analysis of covariance. The course will stress the use of computer packages to solve real-world problems.
Spring 2023, Fall 2023
Discrete probability models. Review of discrete and continuous probability. Conditional expectations. Simulation techniques for random variables. Discrete time stochastic processes: random walks and Markov chains with applications to Monte Carlo simulation and mathematical finance. Introduction to Poisson process.
Summer 2022
Continuous models. Continuous time stochastic processes: Poisson process, Markov chains, Renewal process, Brownian motion, including simulation of these processes. Applications to Black-Scholes model, insurance and ruin problems and related topics.
Summer 2023, Fall 2023
Introduction to fixed Income Markets. Topics include: measurement of interest, annuities certain, varying annuities, amortization schedules, sinking funds, bonds and related securities, depreciation.
Winter 2022, Spring 2023
Problem solving sessions to prepare students for the first four actuarial examinations. Topics corresponding to these examinations (probability, financial mathematics, statistical modeling, and risk management) will be offered in different quarters.
Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Spring 2023