A wealth tracking approach to portfolio management and comparisons of investment strategies

Abstract

This thesis is concerned with several aspects of portfolio management, where the portfolio management process is introduced in Chapter 1. Two important approaches in the modern portfolio management, namely, the mean-variance approach and the expected utility maximization, are presented in Chapter 2 together with some comparisons between these two approaches which finally result in several simple but fundamental questions and lead to the derivation of relationship between the global mean-variance efficient portfolio and the expected utility maximization problem. Chapter 3 is devoted to a particu- lar investment strategy which enables the investor to track a target wealth process and render smallest the deviation from the target. In a very simple setting, namely in the case that only two assets are under consideration and all coefficients of market are constants, an explicit solution for this invest- ment strategy is obtained by using the dynamic programming approach. In addition, some properties are discussed and a generalized strategy is stud- ied in order to achieve more complicated investment objectives. Chapter 4 involves several continuous-time investment strategies derived from various problems including the mean-variance problem, the Merton’s problem, the wealth tracking problem etc and some comparisons are made subsequently.