Asset Management Via Risk-sensitive Control in a Jump-diffusion Model
Risk-sensitive control provides an approach to asset management that in some sense combines the virtues of a Merton-style stochastic control with those of a Markowitz-style mean-variance analysis. In this paper we study a model in which asset prices are represented by a vector jump-diffusion process with growth rates depending on an exogenous process of economic factors, also represnted by a diffusion or jump-diffusion model. When jumps are absent, the model reduces to the one studied by Kuroda and Nagai (Stochastics 2004) where the solution reduces to solving a matrix Riccati equation as in LQG control. When jumps are present, the explicit solution is lost but we are left with a stochastic control problem of dimension equal to the
(small) dimension of the factor process. With no jumps in the factor process this is a uniformly elliptic controlled diffusion, and the Bellman equation has a classical solution. When there are jumps in the factor process as well as in the asset price process, the Bellman equation has a unique viscosity solution. This is joint work with Sebastien Lleo.
Mark Davis, Imperial College London, United Kingdom