Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Risk Sensitive Portfolio Management with Cox--Ingersoll--Ross Interest Rates: The HJB Equation
SIAM Journal on Control and Optimization
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This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai, and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance). By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of this paper is to show that the risk-sensitive jump-diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a partial integro-differential equation, and that this PDE admits a classical $(C^{1,2})$ solution.