Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps

Abstract

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 [12] 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 [13].

arXiv comment32 pages

References in corpus (5)

• Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
• A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
• Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE
• A monotone scheme for high-dimensional fully nonlinear PDEs
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Cited by in corpus (12)

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• Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic control
• Stochastic Near-Optimal Controls for Path-Dependent Systems
• Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps
• Solving non-Markovian Stochastic Control Problems driven by Wiener Functionals
• Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
• Backward SDEs and infinite horizon stochastic optimal control
• Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes
• Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity