International Journal of Control, Vol.87, No.4, 693-703, 2014
Relationship between maximum principle and dynamic programming for stochastic differential games of jump diffusions
This paper is concerned with the relationship between maximum principle and dynamic programming for zero-sum stochastic differential games of jump diffusions. Under the assumption that the value function is smooth enough, relations among the adjoint processes, the generalised Hamiltonian function and the value function are given. A portfolio optimisation problem under model uncertainty in an incomplete financial market is discussed to show the applications of our result.
Keywords:dynamic programming;stochastic differential games;model uncertainty;portfolio optimisation;stochastic optimal control;jump diffusions;maximum principle;backward stochastic differential equation