Optimal control theory with applications in portfolio and consumption optimization

Abstract

The main goal of a financial portfolio manager is to construct a high return portfolio. Additionally, different consumers have different risk exposure, which the portfolio manager has to identify and construct a portfolio well suited for their clients. Moreover, retirees have to spend their savings in the most efficient way. This can be done by maximizing their utility of consumption. This thesis treats the maximization the utility of consumption in two different methods. The first uses Calculus of variations and the other is using the maximum principle. On the other hand, financial portfolios were created using discrete and continuous maximum principle, and convex optimization. Finally, an example using stochastic optimal control constructs a portfolio using a risky asset and a risk free asset. One cannot compare the different methods used to construct the portfolios, because they all account for the risk differently. It is up to the portfolio manager to decide which methods to use.