Jump-diffusion Risk-sensitive Asset Management II: Jump-diffusion Factor Model
In this paper, the authors extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. 2 (2011) 22-54] by allowing jumps in the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a Partial Integro-Differential Equation (PIDE). By combining viscosity solutions with a change of notation, a policy improvement argument and classical results on parabolic PDEs, they prove that the HJB PIDE admits a unique smooth solution. A verification theorem concludes the resolution of this problem.