Geodesic
Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1073-1096.

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This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.

DOI : 10.1051/cocv/2011204
Classification : 93E20, 60H10, 34K50
Keywords: stochastic optimal control, maximum principle, stochastic differential delayed equation, anticipated backward differential equation, fully coupled forward-backward stochastic system, Clarke generalized gradient 
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Huang, Jianhui; Shi, Jingtao. Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1073-1096. doi : 10.1051/cocv/2011204. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011204/

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