Numerical approximation of the value of a stochastic differential game with asymmetric information

TL;DR

This paper develops a probabilistic numerical scheme to approximate the value function of a zero-sum differential game with asymmetric information, ensuring convergence to the unique viscosity solution and demonstrating its effectiveness through numerical experiments.

Contribution

It introduces a convexity-preserving probabilistic numerical scheme for a complex stochastic differential game with asymmetric information, extending previous methods.

Findings

The scheme converges to the unique viscosity solution.

The fully discrete approximation is implementable and accurate.

Numerical experiments validate the scheme's properties.

Abstract

We consider a convexity constrained Hamilton-Jacobi-Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the approximation of the value function which is discrete w.r.t. the time and convexity variables, and show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semi-discrete scheme to obtain an implementable fully discrete numerical approximation of the value function and present numerical experiments to demonstrate the properties of the proposed numerical scheme.