Stochastic maximum principle for SPDEs with delay

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Guatteri, Giuseppina¹  Masiero, Federica²  Orrieri, Carlo³ 

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy

[3] Sapienza Univ Roma, Dipartimento Matemat, Piazzale Aldo Moro 5, I-00185 Rome, Italy

关键词: Stochastic maximum principle;    Stochastic delay differential equation;    Anticipated backward stochastic differential equations;    Infinite dimensions;   

DOI  :  10.1016/j.spa.2016.11.007

来源: Elsevier

【 摘 要 】

In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional stochastic evolution equations with delay in the state. In the cost functional we allow the final cost to depend on the history of the state. To treat such kind of cost functionals we introduce a new form of anticipated backward stochastic differential equations which plays the role of dual equation associated to the control problem. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free