Risk Sensitive Asset Management With Constrained Trading Strategies

This paper presents an application of risk sensitive control theory in financial decision making. A variation of Merton's continuous-time intertemporal capital asset pricing model is investigated where the investor's infinite horizon objective is to maximize the portfolio's risk adjusted growth rate. In earlier studies it was assumed either that the residuals associated with the assets are uncorrelated with the residuals associated with the factors or that there are no exogenous constraints like short selling restrictions. Here we develop computational procedures for the case where both of these assumptions are removed. Our approach is to first approximate the continuous time problem with a discrete time controlled Markov chain. We then solve the latter using the method of successive approximations for risk sensitive Markov decision chains. We show by numerical example that our approach is feasible, at least for cases where there are only a few factors. Our results suggest that when the hedging term is dominated by the myopic term for the corresponding unconstrained problem, then the optimal strategy computed for the constrained problem differs very little from the optimal myopic strategy for the same constrained problem.