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
收藏
页码：572 / 596
页数：25
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