Maximum principle for optimal control of anticipated forward-backward stochastic differential delayed systems with regime switching

被引：19

作者：

Lv, Siyu ^{[1
]}

Tao, Ran ^{[1
]}

Wu, Zhen ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

OPTIMAL CONTROL APPLICATIONS & METHODS | 2016年 / 37卷 / 01期

关键词：

forward-backward stochastic system; maximum principle; regime switching; Markov chain; stochastic differential equation with delay; anticipated backward stochastic differential equation; EQUATIONS; INVESTMENT; JUMPS; MODEL;

D O I：

10.1002/oca.2160

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with a Pontryagin maximum principle for optimal control problem of stochastic system, which is described by an anticipated forward-backward stochastic differential delayed equation and modulated by a continuous-time finite-state Markov chain. We establish a necessary maximum principle and sufficient verification theorem for the optimal control by virtue of the duality method and convex analysis. To illustrate the theoretical results, we apply them to a recursive utility investment-consumption problem, and the optimal consumption rate is derived explicitly. Copyright (C) 2015 John Wiley & Sons, Ltd.

引用

页码：154 / 175

页数：22

共 36 条

[1]

[Anonymous], 1999, STOCHASTIC CONTROLS

[2] A delayed Black and Scholes formula [J].