Financial benchmark tracking problems under a stochastic linear quadratic control framework

Abstract

In this thesis we analyse the problem of tracking a financial benchmark via trading a portfolio of a small number of assets on a finite time horizon. The development of general stochastic linear quadratic control (SLQ) theory in recent years allows us to study this investment problem using this approach. We formulate the problem under the SLQ control framework and derive an optimal feedback control solution using stochastic Riccati equations and an accompanying equation. We then apply our theory to benchmark problems involving tracking a continuously compounded given growth rate and a stock market index to obtain novel solutions. An outline of how we might implement the model in practice is also given.