Additional units offered through the Key Centre for Statistical Science

Stochastic Processes 2

Dr Aidan Sudbury
Aidan.Sudbury@sci.monash.edu.au

Random Walks, Markov Chains, Martingales Computation in Financial Mathematics

Course outline

Stochastic differential equations. Wiener process. Numerical method. Taylor expansion of stochastic differential equations. Strong solution. Weak solution. Mean-square stability property. Monte Carlo simulation method. Evaluation of option values. European option. American option. Optimisation methods. Calibration. The method of moments. Maximum-likelihood method. Computer programming. MATLAB. C++.

Prerequisites

Some knowledge of probability is required and some knowledge of financial mathematics is desirable.

References

• F Klebaner, Introduction to stochastic calculus with applications, 2nd edition, Imperial College Press, 2005.
• PE Kloeden, E Platen, H Schurz, Numerical solution of SDE through computer experiments, Springer-Varlag, 1994.
• R Seydel, Tools for computational finance, Springer, 2002.

Statistical Inference

Foundations of probability, limit theorems, asymptotics.