Multiperiod portfolio optimization in stochastic markets using the mean-variance approach

Abstract

ABSTRACT In this thesis, several umltiperiod portfolio optimization problems are considered where 9 the investors try to achieve their goal at the end of the investment horizon. The market consists of a riskless asset and several risky assets whose returns have a mean vector and a (»variance matrix both of which depend on the prevailing market conditions described by a Markov chain. The returns are therefore serially correlated with each other via this stodiastic market. Various objectives including the safety-first approach, the coefficient of variation and the quadratic utility function are considered. The common feature of the objective functions analyzed in this thesis is that they are formulated using the mean and the variance of the final wealth at the end of the investment horizon, which also corresponds to the final portfolio return if the initial wealth is taken to be one. An auxiliary problem is formulated and solved to find the optimal portfolios and generate the efficient frontier. Op timal portfolio management policies and the implied optimal mean and variance of the final wealth are found analytically for each problem. Illustrative cases are given to demonstrate the solution procedure, and the optimal policies are interpreted for each problem. in