Clayton First semester 2008 (Day)
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. Risk models in insurance. Ruin probability bound. Principles of simulation. Use of Excel packages.
On the completion of this unit, students will gain an understanding of the methods of modern probability and random processes, and develop skills for modelling of random systems. Students will be able to apply this knowledge and skills in the context financial and insurance modelling.
Assignments: 20%
final exam (three hour): 80%
Three 1-hour lectures and one 1-hour support class per week
MTH1030 and one of STA2022, MTH2032, MTH2010
ETC3510, ETC3514