
arXiv: 1110.1588
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 $(t,x)\in��\times\R^d$, for all compact time intervals $��$ 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.
25 pages
Statistics and Probability, Time change, Viscosity solution, Applied Mathematics, Probability (math.PR), Backward stochastic differential equations, Kulik transformation, Lipschitz continuity, Poisson random measure, 35D10, 60H30, 93E20, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), Semiconcavity, Modelling and Simulation, Value function, FOS: Mathematics, Brownian motion, Mathematics - Optimization and Control, Mathematics - Probability, Analysis of PDEs (math.AP)
Statistics and Probability, Time change, Viscosity solution, Applied Mathematics, Probability (math.PR), Backward stochastic differential equations, Kulik transformation, Lipschitz continuity, Poisson random measure, 35D10, 60H30, 93E20, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), Semiconcavity, Modelling and Simulation, Value function, FOS: Mathematics, Brownian motion, Mathematics - Optimization and Control, Mathematics - Probability, Analysis of PDEs (math.AP)
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