A maximum principle approach to stochastic H2/H∞ control with random jumps

A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.