Risk-sensitive Portfolio Optimization with Full and Partial Information

Abstract

We discuss an application of risk-sensitive control to portfolio optimization problems for a general factor model, which is considered a variation of Merton's intertemporal capital asset pricing model ([18]). In the model the instantaneous mean returns as well as volatilities of the security prices are affected by economic factors and the security prices. The economic factors are assumed to satisfy stocahstic differential equations whose coefficients depend on the security prices as well as themselves. In such general incomplete market models under Markovian setting we consider constructing optimal strategies for risk-sensitive portfolio optimization problems on a finite time horizon. We study the Bellman equations of parabolic type corresponding to the optimization problems. Through analysis of the Bellman equations we construct optimal strategies from the solution of the equation. We further discuss the problem with partial information. We shall obtain a necessary condition for optimality using backward stochastic partial differential equations.