2011/02/24 by Mark H. Davis, Davis, Mark, Sébastien Lleo +2
Decision Sciences · Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Electrical engineering #FOS: Mathematics #Financial Risk and Volatility Modeling #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1102.5126
openalex publication_date 2011/02/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this article we extend earlier work on the jump-diffusion risk-sensitive\nasset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in\nboth the factor process and the asset prices, as well as stochastic volatility\nand investment constraints. In this case, the HJB equation is a partial\nintegro-differential equation (PIDE). By combining viscosity solutions with a\nchange of notation, a policy improvement argument and classical results on\nparabolic PDEs we prove that the HJB PIDE admits a unique smooth solution. A\nverification theorem concludes the resolution of this problem.\n