  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.
