Relationship between Maximum Principle and Dynamic Programming in Stochastic Differential Games and Applications

摘要

This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.