Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic System with Delay
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- 英文论文题名：Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic System with Delay
- 论文作者：Na Li ; Guangchen Wang ; Zhen Wu
- 英文论文作者：Na Li ; Guangchen Wang ; Zhen Wu ; School of Statistics ; Shandong University of Finance and Economics ; School of Control Science and Engineering ; Shandong University ; School of Mathematics ; Shandong University
- 年：2017
- 作者机构：School of Statistics,Shandong University of Finance and Economics;School of Control Science and Engineering,Shandong University;School of Mathematics,Shandong University;
- 英文论文关键词：Stochastic optimal control ; linear-quadratic problem ; forward-backward stochastic system with delay
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O232
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：670k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with an optimal control problem of anticipated forward-backward stochastic differential equation with delay. We obtain an explicit representation of optimal control for delayed problem first, and then use it to solve a delayed cash management problem with recursive utility. The explicit optimal control strategy of the investor is given and some numerical simulations are used to illustrate the influence of the time delay on optimal solution.
This paper is concerned with an optimal control problem of anticipated forward-backward stochastic differential equation with delay. We obtain an explicit representation of optimal control for delayed problem first, and then use it to solve a delayed cash management problem with recursive utility. The explicit optimal control strategy of the investor is given and some numerical simulations are used to illustrate the influence of the time delay on optimal solution.
This paper is concerned with an optimal control problem of anticipated forward-backward stochastic differential equation with delay. We obtain an explicit representation of optimal control for delayed problem first, and then use it to solve a delayed cash management problem with recursive utility. The explicit optimal control strategy of the investor is given and some numerical simulations are used to illustrate the influence of the time delay on optimal solution.
引文
[1]L.Chen and Z.Wu,“Maximum principle for the stochastic optimal control problem with delay and application”,Automatica,Vol.46,pp.1074-1080,2010.
[2]Y.Hu and S.Peng,“Solution of forward-backward stochastic differential equations”,Probability Theory and Related Fields,Vol.103,No.2,pp.273-283,1995.
[3]N.Li and Z.Wu,“Maximum principle for anticipated recursive stochastic optimal control problem with delay and L évy processes”,Applied Mathematics a Journal of Chinese Universities Ser.B,Vol.29,No.1,pp.67-85,2014.
[4]N.Li and Z.Yu,“Recursive stochastic linearquadratic optimal control and nonzero-sum differential game problems with random jumps”,Advances in Difference Equations,Vol.144,pp.1-19,2015.
[5]S.Lv,R.Tao and Z.Wu,“Maximum principle for optimal control of anticipated forwardbackward stochastic differential delayed systems with regime switching”,Optimal Control Applications and Methods,Vol.37,pp.154-175,2016.
[6]B.?ksendal and A.Sulem,“A maximum principle for optimal control of stochastic systems with delay,with applications to finance”,Optimal control and partial differential equations,pp.64-79,Amsterdam:ISO Press,2000.
[7]S.Peng and Z.Yang,“Anticipated backward stochastic differential equations”,The Annals of Probability,Vol.37,pp.877-902,2009.
[8]S.Peng and Z.Wu,“Fully coupled forwardbackward stochastic differential equations and applications to optimal control”,SIAM Journal on Control and Optimization,Vol.37,No.3,pp.825-843,1999.
[9]G.Wang and H.Xiao,“Arrow sufficient conditions for optimality of fully coupled forwardbackward stochastic differential equations with applications to finance”,Journal of Optimization Theory and Applications,Vol.165,pp.639-656,2015.
[10]S.Wang and Z.Wu,“Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls”,Journal of Systems Science and Complexity,Vol.30,pp.280-306,2017.
[11]Z.Yu,“The stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls”,Automatica,Vol.48,pp.2420-2432,2012.
[2]Y.Hu and S.Peng,“Solution of forward-backward stochastic differential equations”,Probability Theory and Related Fields,Vol.103,No.2,pp.273-283,1995.
[3]N.Li and Z.Wu,“Maximum principle for anticipated recursive stochastic optimal control problem with delay and L évy processes”,Applied Mathematics a Journal of Chinese Universities Ser.B,Vol.29,No.1,pp.67-85,2014.
[4]N.Li and Z.Yu,“Recursive stochastic linearquadratic optimal control and nonzero-sum differential game problems with random jumps”,Advances in Difference Equations,Vol.144,pp.1-19,2015.
[5]S.Lv,R.Tao and Z.Wu,“Maximum principle for optimal control of anticipated forwardbackward stochastic differential delayed systems with regime switching”,Optimal Control Applications and Methods,Vol.37,pp.154-175,2016.
[6]B.?ksendal and A.Sulem,“A maximum principle for optimal control of stochastic systems with delay,with applications to finance”,Optimal control and partial differential equations,pp.64-79,Amsterdam:ISO Press,2000.
[7]S.Peng and Z.Yang,“Anticipated backward stochastic differential equations”,The Annals of Probability,Vol.37,pp.877-902,2009.
[8]S.Peng and Z.Wu,“Fully coupled forwardbackward stochastic differential equations and applications to optimal control”,SIAM Journal on Control and Optimization,Vol.37,No.3,pp.825-843,1999.
[9]G.Wang and H.Xiao,“Arrow sufficient conditions for optimality of fully coupled forwardbackward stochastic differential equations with applications to finance”,Journal of Optimization Theory and Applications,Vol.165,pp.639-656,2015.
[10]S.Wang and Z.Wu,“Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls”,Journal of Systems Science and Complexity,Vol.30,pp.280-306,2017.
[11]Z.Yu,“The stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls”,Automatica,Vol.48,pp.2420-2432,2012.