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Relationship between Maximum Principle and Dynamic Programming in Stochastic Differential Games and Applications
School of Mathematics, Shandong University, Jinan, China
- 1 School of Mathematics, Shandong University, Jinan, China
American Journal of Operations Research·Volume 03 (2013)·Pages 445–453·Published 24 October 2013·DOI10.4236/ajor.2013.36043
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Abstract
This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum sto chastic 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.
KeywordsStochastic Optimal ControlStochastic Differential GamesDynamic ProgrammingMaximum PrinciplePortfolio OptimizationModel Uncertainty
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