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.