Risk-sensitive dynamic asset management

This paper develops a continuous time portfolio optimization model where th e mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's r eturn on equity, interest rates, and unemployment rates. In particular, the factors are Gaussian processes, and the drift coefficients for the securit ies are affine functions of these factors. We employ methods of risk-sensit ive control theory, thereby using an infinite horizon objective that is nat ural and features the long run expected growth rate, the asymptotic varianc e, and a single risk-aversion parameter. Even with constraints on the admis sible trading strategies, it is shown that the optimal trading strategy has a simple characterization in terms of the factor levels. For particular fa ctor levels, the optimal trading positions can be obtained as the solution of a quadratic. program. The optimal objective value, as a function of the risk-aversion parameter, is shown to be the solution of a partial different ial equation. A simple asset allocation example, featuring a Vasicek-type i nterest rate which affects a stock index and also serves as a second invest ment opportunity, provides some additional insight about the risk-sensitive criterion in the context of dynamic asset management.