MA6000D: Stochastic Optimal Control and Applications in Finance 
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This graduate course will aim to cover some of the fundamental probabilistic tools for the understanding of Stochastic Optimal Control problems, and give an overview of how these tools are applied in solving particular problems. Since many of the important applications of Stochastic Control are in financial applications, we will concentrate on applications in this field. This course will be suitable for students with a strong undergraduate background in probability and stochastic processes, but we will provide a brief introduction to important underpinning theoretical ideas such as stochastic integration, Itô's Lemma, martingale representation theorem, stochastic differential equations, diffusions and the FeynmanKac formula, however we will try to cover material quickly, and so the presentation of these ideas will be a bit informal. The course will roughly break into two parts: after some motivation and discussion of introductory problems, we will review much of the background theory: in particular, we will provide an overview of stochastic integration in a Brownian filtration, and some SDE theory and key results, following the presentation in Øksendal's book . We will then review some of the key results in Stochastic optimal control, following the presentation in Chapter 11 of this book. To see some of the important applications in Finance, we will use Karatzas and Shreve , "Methods of Mathematical Finance" and in some circumstances, directly refer to research papers. The course is timetabled at 10:1512.05 on Wednesdays in 4W1.7 . An approximate outline of the lectures is as follows:
It is expected/hoped that some volunteers will prepare some of the later lectures, and the list will be updated as the semester progresses. 
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Last updated: 8/10/12
Maintainer:
Alex Cox