Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE
Kharroubi, Idris; Pham, Huyen (2015), Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE, Annals of Probability, 43, 4, p. 1823-1865. 10.1214/14-AOP920
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1212.2000v3
Journal nameAnnals of Probability
Institute of Mathematical Statistics
MetadataShow full item record
Abstract (EN)We aim to provide a Feynman-Kac type representation for Hamilton-Jacobi-Bellman equation, in terms of Forward Backward Stochastic Differential Equation (FBSDE) with a simulatable forward process. For this purpose, we introduce a class of BSDE where the jumps component of the solution is subject to a partial nonpositive constraint. Existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions. We then show how minimal solution to this BSDE class provides a new probabilistic representation for nonlinear integro-partial differential equations (IPDEs) of Hamilton-Jacobi-Bellman (HJB) type, when considering a regime switching forward SDE in a Markovian framework. Moreover, we state a dual formula of this BSDE minimal solution involving equivalent change of probability measures. This gives in particular an original representation for value functions of stochastic control problems including controlled diffusion coefficient.
Subjects / Keywordsnonlinear Integral PDE; Hamilton-Jacobi-Bellman equation; regime-switching jump-diffusion; onstrained BSDE; viscosity solutions; inf-convolution; semiconcave approximation; BSDE with jumps
Showing items related by title and author.
L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1 Bokanowski, Olivier; Forcadel, Nicolas; Zidani, Hasnaa (2010) Article accepté pour publication ou publié