Approximate value iteration approaches to constrained dynamic portfolio problems

Abstract

This thesis considers a discrete-time, finite-horizon dynamic portfolio problem where an investor makes sequential investment decisions with the goal of maximizing expected terminal wealth. We allow non-standard utility functions and constraints upon the portfolio selections at each time. These problem formulations may be computationally difficult to address through traditional optimal control techniques due to the high dimensionality of the state space and control space. We consider suboptimal solution methods based on approximate value iteration. The primary innovation is the use of mean-variance portfolio selection methods. We present two case studies that employ these approximate value iteration methods. The first case study explores the effect of an insolvency constraint that prohibits further investing when an investor reaches non-positive wealth. When the investor has an exponential utility function, the insolvency constraint leads to more conservative investment policies when there are many investment periods remaining, except when wealth is very low. The second case study explores the effects of dollar position constraints that represent limited liquidity in certain investment strategies. When the investor has a CRRA utility function, we find that these constraints lead to non-myopic policies that are more conservative than the constrained myopic policy.