This course covers 1) uni-variate probability distributions, including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal, gamma, Weibull, and normal; 2) multivariate joint distributions, conditional and marginal distributions; 3) moments and moment generating function, 4) transform of variables, 5) order statistics, and 6) central limit theorem. The purpose of this course of reading is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of probability topics and the supporting calculus is assumed.

This course introduces quantitative methods for pricing financial derivatives, treating in detail the program of valuation by “no-arbitrage.” Institutional features of derivative markets are covered along with theory and application. The discrete-time binomial pricing model is studied in depth. An introduction to the elements of stochastic calculus (Brownian Motion, and Ito’s formula) then enables students to work with the mainstream continuous-time models of Black-Scholes-Merton and others. These methods are applied to price and hedge standard securities such as stock options, interest rate caps, swaps, swaptions, and commodity futures. Students will see application to insurance and actuarial science. The course will cover Society of Actuaries required reading.