Portfolio Optimization Applications of Stochastic Receding Horizon Control

Abstract

This paper develops stochastic receding horizon control for constrained dynamic portfolio optimization problems. In particular, we formulate two portfolio optimization problems. The first is that of risk adjusted wealth maximization, while the second is the problem of optimally tracking an index of stocks with fewer stocks. We consider both of these problems subject to probabilistic chance constraints. By modeling the dynamics in the problems as linear systems subject to state and control multiplicative noise, and approximating linear chance constraints with quadratic expectation constraints, we show that both can be approached using stochastic receding horizon control. In particular, we use a closed loop version of stochastic receding horizon control where the on-line optimization is solved as a semi-definite program. Numerical examples demonstrate the computations involved in these problems and indicate that stochastic receding horizon control is a promising new approach to constrained portfolio optimization problems.