Optimal asset allocation strategies for investments within the local asset market

Abstract

The need for mathematical models in the financial industry including the portfolio industry has increased over the past years with the increase in the rate of fund failures. This dissertation will focus mainly on portfolio optimization and asset allocation strategies in order to find the optimal capital weightings for a basket of investments that maximizes the investor's utility and wealth at final horizon. The randomness of financial markets and geometric Brownian motions provided the motivation for a mathematical study of stock price modelling using Brownian motion and stochastic calculus. This is a relatively new field and for this thesis, applications of stochastic calculus were used in order to predict stock prices. Following this, stochastic portfolio theory was utilized in order to provide an insight for portfolio behaviour and equity market structure so as to help in modelling the dynamics of stock portfolios. Finally, stochastic optimal control was considered in order to try to find the best investing strategy with the best allocation of investments into different assets which maximizes the investor's utility where we assume that an investor makes investment decisions based on CRRA utility functions. In order to do so, the solution using dynamical programming will furnish a solution to the optimal maximization problem. This leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation where the solution of this equation results in an optimal asset allocation strategy. As an application of stochastic optimal control, a pure investment policy for a constant absolute risk aversion (CRRA) investor who faces no transaction costs when trading multiple risky assets will be applied to the Maltese equity market.