完全耦合正倒向随机控制系统的动态规划原理与最大值原理之间的联系

doi:10.6040/j.issn.1671-9352.0.2015.383

Abstract

Abstract: This paper is concerned with the connection between dynamic programming principle(DPP)and maximum principle(MP)for the forward-backward stochastic control system, where the recursive cost functional is defined as one of the solution to a controlled fully coupled forward-backward stochastic differential equation(FBSDE). With some smooth assumptions, relations among the value function, generalized Hamiltonian function and adjoint processes are given, when the diffusion coefficient of the forward equation does not contain the state variable z. The general case for the problem is open. A linear example is discussed as the illustration of our main result.

Key words: fully coupled forward-backward stochastic differential equation, maximum principle, stochastic optimal control, dynamic programming principle

CLC Number:

O241.82

NIE Tian-yang, SHI Jing-tao. The connection between DPP and MP for the fully coupled forward-backward stochastic control systems[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 121-129.

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The connection between DPP and MP for the fully coupled forward-backward stochastic control systems

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