Stochastic Maximum Principle of Near‐Optimal Control of Fully Coupled Forward‐Backward Stochastic Differential Equation

Maoning Tang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: This paper first makes an attempt to investigate the near‐optimal control of systems governed by fully nonlinear coupled forward‐backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any ε‐near optimal control in a local form with an error order of exact ε1/2. Moreover, under additional convexity conditions on Hamiltonian function, we prove that an ε‐maximum condition in terms of the Hamiltonian in the integral form is sufficient for near‐optimality of order ε1/2.

Date: 2014
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https://doi.org/10.1155/2014/361259

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:361259

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