Stochastics examines phenomena in which chance plays a central role. The theory of stochastic phenomena has applications in engineering systems, the physical and life sciences and economics, to give just a few examples. Applications of stochastic processes arise particularly naturally in finance where there are fluctuations in stock prices and practitioners are required to solve different types of optimisation problems in stochastically driven systems. For this reason, it is particularly important that mathematicians in general and especially mathematicians specialising in problems in the financial industry are equipped with tools to analyse and quantify random phenomena. This unit will expose you to critical topics in the theory and application of stochastic processes and analysis in mathematical finance. You will learn how to identify problems that require the application of stochastic theory, how to rigorously describe such problems using appropriate mathematical frameworks and how to tackle and solve the problem once it has been phrased in terms of stochastic theory. Along the way, you will also gain a deep knowledge about diverse topics in finance and the relevance of mathematical analysis in the financial industry.
lecture 3 hrs/week, tutorial 1 hr/week for 13 weeks
2 xassignment (20% each, 40% total), final exam (60%)
This unit is only available in odd years.
Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent.