Comparison theorem of solutions to BSDE with jumps, and viscosity solution to a generalized Hamilton-Jacobi-Bellman equation (Q2712233)

For a system of controlled forward-backward stochastic differential equations \((x_s^{t,x,v}, y_s^{t,x,v})\) with jump parts, the value function NEWLINE\[NEWLINEu(t,x)= \sup_v y_s^{t,x,v}|_{s=t}NEWLINE\]NEWLINE is shown to be a viscosity solution of the HJB-equation associated with the control problem. The result is derived by applying a quite general form of a comparison theorem for BSDE's.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].