In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem by allowing for jumps in both the factor process and the asset prices as well as stochastic volatility and investment constraints. In this case, the HJB equation is a PIDE.By combining viscosity solutions with a change of notation, a policy improvement argument and classical results on parabolic PDEs we prove that the PIDE admits a unique smooth solution. A verification theorem concludes the resolutions of this problem .
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 the 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 PIDE, and that this PDE admits a classical C^{1,2 .
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In this article we extend earlier work on the jump-diffusion
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
R
asset management problem by allowing for jumps in both the factor process and the asset prices as well as stochastic volatility and investment constraints. In this case, the HJB equation is
optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using
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PIDE.By combining viscosity solutions with a
R
notation, a policy improvement argument and classical results on parabolic PDEs we prove that the PIDE admits a unique smooth solution. A verification theorem concludes the resolutions of this problem
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 the 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 PIDE, and that this PDE admits a classical C^{1,2