Abstract and Applied Analysis (Jan 2012)

A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

  • Shaolin Ji,
  • Qingmeng Wei,
  • Xiumin Zhang

DOI
https://doi.org/10.1155/2012/537376
Journal volume & issue
Vol. 2012

Abstract

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We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.