OPTIMAL CONTROL OF STOCHASTIC DELAY EQUATIONS AND TIME-ADVANCED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

被引：83

作者：

Oksendal, Bernt ^{[1
,2
]}

Sulem, Agnes ^{[3
]}

Zhang, Tusheng ^{[4
]}

机构：

[1] Univ Oslo, CMA, N-0316 Oslo, Norway

[2] Norwegian Sch Econ & Business Adm, Bergen, Norway

[3] INRIA Paris Rocquencourt, F-78153 Le Chesnay, France

[4] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

来源：

ADVANCES IN APPLIED PROBABILITY | 2011年 / 43卷 / 02期

基金：

欧洲研究理事会;

关键词：

Optimal control; stochastic delay equation; Levy process; maximum principle; Hamiltonian; adjoint process; time-advanced BSDE;

D O I：

10.1239/aap/1308662493

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study optimal control problems for (time-)delayed stochastic differential equations with jumps. We establish sufficient and necessary stochastic maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-)advanced backward stochastic differential equation (ABSDE). Several results on existence and uniqueness of such ABSDEs are shown. The results are illustrated by an application to optimal consumption from a cash flow with delay.

引用

页码：572 / 596

页数：25

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