Introductory description

An example of a stochastic control problem is the ‘Red and Black’ problem. Essentially, this asks what the best betting strategy is if you want to maximise your chance of winning £1000 playing roulette.

This module is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.

Prerequisites: ST318 Probability Theory AND ST333 Applied Stochastic Processes.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Recapitulation of the theory of stochastic processes.
Introduction to finite horizon control problems and optimal stopping.
The Hamilton-Jacobi-Bellman equation.
Infinite horizon discounted problems.
Applications to finance, clinical trials, planning production processes and insurance, and, time permitting
Discussion of long-run average problems.

Learning outcomes

By the end of the module, students should be able to:

• Identify and to deal with stochastic control and optimal stopping problems.
• Solve simple Hamilton-Jacobi-Bellman equations.
• Apply the above techniques to finance, to clinical trials and to the planning of production processes.

Indicative reading list

Reading lists can be found in Talis

Specific reading list for the module

Subject specific skills

TBC

Transferable skills

TBC