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This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.
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참고문헌 (16)
참고문헌 신청
A. Bensoussan / 1981 / Nonlinear filtering and stochastic control / Springer :1~62
Li Chen / 2015 / Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation / Journal of Optimization Theory and Applications 167(3):1112~1135
J. Cvitanic / 1998 / Backward stochastic differential equations with constraints on the gains-process / Ann. Probab 26(4):1522~1551
Łukasz Delong / 2010 / Backward stochastic differential equations with time delayed generators—results and counterexamples / The Annals of Applied Probability 20(4):1512~1536
M. Fuhrman / 2004 / Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces / Ann. Probab 32(1B):607~660
Li Chen / 2015 / Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation / Journal of Optimization Theory and Applications 167(3):1112~1135
J. Cvitanic / 1998 / Backward stochastic differential equations with constraints on the gains-process / Ann. Probab 26(4):1522~1551
Łukasz Delong / 2010 / Backward stochastic differential equations with time delayed generators—results and counterexamples / The Annals of Applied Probability 20(4):1512~1536
M. Fuhrman / 2004 / Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces / Ann. Probab 32(1B):607~660
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