Random variables, application to models of random payoffs. Conditional expectation. Normal distribution and multivariate normal distribution. Best predictors. Stochastic (random) processes. Random walk. Limit theorems. Brownian motion. Ito integral and Ito's formula. Black-Scholes, Ornstein-Uhlenbeck process and Vasicek's stochastic differential equations. Martingales. Gambler's ruin. Fundamental theorems of Mathematical Finance. Binomial and Black-Scholes models. Models for Interest Rates. Risk models in insurance. Ruin probability bound. Principles of simulation. Use of Excel package. -- Course Website
Instructor: Professor Fima Klebaner
Prerequisites: One of MTH1030, MTH1035 or ETC2440 and one of MTH2010, MTH2015, MTH2032, MTH2222 or ETC2520. Either MTH2222 or ETC2520 is highly recommended.
