Necessary and Sufficient Optimality Conditions for Relaxed and Strict Control of Forward-Backward Doubly SDEs with Jumps Under Full and Partial Information  

作　　者：AL-HUSSEIN AbdulRahman GHERBAL Boulakhras 

机构地区：[1]Department of Mathematics,College of Science,Qassim University,Buraydah 51452,Saudi Arabia [2]Laboratory of Mathematical Analysis,Probability and Optimization,University of Mohamed Khider,Biskrua07000,Algeria

出　　处：《Journal of Systems Science & Complexity》2020年第6期1804-1846,共43页系统科学与复杂性学报（英文版）

基　　金：Qassim University,represented by the Deanship of Scientific Research under Grant No.SR-D-015-3352;the Algerian PRFU under Grant No.C00L03UN07120180005。

摘　　要：This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.

关 键 词：Adjoint equations forward-backward doubly stochastic differential equations maximum principle necessary conditions Poisson process relaxed control strict control sufficient conditions 

分 类 号：O232[理学—运筹学与控制论] O211.63[理学—数学]