2011/10/07 by Shuai Jing, Jing, Shuai
Economics, Econometrics and Finance · Mathematics · Social Sciences · #35D10 #60H30 #93E20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.AP #math.OC #math.PR #msc:35D10 #msc:60H30 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1110.1588
25 pages
arxiv created 2011/10/07 · openalex publication_date 2011/10/07 · arxiv updated 2011/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the regularity properties of integro-partial differential equations of Hamilton-Jocobi-Bellman type with terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a Brownian motion and a compensated Poisson random measure. More precisely, we prove that, under appropriate assumptions, the viscosity solution of such equations is jointly Lipschitz and jointly semiconcave in (t,x)∈Δ×\Rd, for all compact time intervals Δ excluding the terminal time. Our approach is based on the time change for the Brownian motion and on Kulik's transformation for the Poisson random measure.