The optimal control problem associated with multi-valued stochastic differential equations with jumps

This work concerns the optimal control problem associated with multi-valued stochastic differential equations with Lévy jumps. Through the Yosida approximation technique, we prove that the value function of the control problem is the unique viscosity solution of a second order parabolic integro-differential equation involving a multi-valued maximal monotone operator. The dynamic programming principle and the comparison theorem are also proved.