Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic control

Abstract

We introduce some sparse grids interpolations used in Semi-Lagrangian schemes for linear and fully non-linear diffusion Hamilton Jacobi Bellman equations arising in stochastic control. We prove that the method introduced converges toward the viscosity solution of the problem and we show that some potentially high order schemes can be efficiently implemented. Numerical test in dimension $2$ to $5$ are achieved and show that deterministic methods can be used efficiently in stochastic control in moderate dimension.

28 pages, 11 figures

References in corpus (2)

• A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
• Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps

Cited by in corpus (1)

• Numerical approximation of BSDEs using local polynomial drivers and branching processes