Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps
Kharroubi, Idris; Langrené, Nicolas; Pham, Huyên (2015), Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps, The Annals of Applied Probability, 25, 4, p. 2301-2338. 10.1214/14-AAP1049
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1311.4505v2
Journal nameThe Annals of Applied Probability
Institute of Mathematical Statistics
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Abstract (EN)We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in  by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation for the value function and for an optimal control in feedback form. We obtained a convergence rate without any ellipticity condition on the controlled diffusion coefficient. Explicit implementable scheme based on Monte-Carlo simulations and empirical regressions, associated error analysis, and numerical experiments are performed in the companion paper [ Monte Carlo Methods Appl. 20 (2014) 145–165].
Subjects / KeywordsDiscrete time approximation; optimal control; nonlinear degenerate PDE; Hamilton-Jacobi-Bellman equation; backward stochastic differential equations.
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