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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

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1311.4505v2
Date
2015
Journal name
The Annals of Applied Probability
Volume
25
Number
4
Publisher
Institute of Mathematical Statistics
Published in
Paris
Pages
2301-2338
Publication identifier
10.1214/14-AAP1049
Metadata
Show full item record
Author(s)
Kharroubi, Idris
Langrené, Nicolas cc
Pham, Huyên
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 [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 [ Monte Carlo Methods Appl. 20 (2014) 145–165].
Subjects / Keywords
Discrete time approximation; optimal control; nonlinear degenerate PDE; Hamilton-Jacobi-Bellman equation; backward stochastic differential equations.

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