TY - JOUR

T1 - Numerical Approximation of the Value of a Stochastic Differential Game with Asymmetric Information

AU - Baňas, Ľubomír

AU - Ferrari, Giorgio

AU - Randrianasolo, Tsiry Avisoa

PY - 2021

Y1 - 2021

N2 - 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 with respect to the time and convexity variables, and we show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semidiscrete 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.

AB - 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 with respect to the time and convexity variables, and we show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semidiscrete 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.

U2 - 10.1137/19M1309997

DO - 10.1137/19M1309997

M3 - Article

VL - 59.2021

SP - 1109

EP - 1135

JO - SIAM journal on control and optimization

JF - SIAM journal on control and optimization

SN - 1095-7138

IS - 2

ER -