A mean-field stochastic maximum principle via Malliavin calculus

被引：91

作者：

Meyer-Brandis, Thilo ^{[1
]}

Oksendal, Bernt ^{[1
,2
]}

Zhou, Xun Yu ^{[3
,4
]}

机构：

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

[2] Norwegian Sch Econ & Business Adm NHH, N-5045 Bergen, Norway

[3] Univ Oxford, Inst Math, Oxford OX1 3LB, England

[4] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2012年 / 84卷 / 5-6期

基金：

欧洲研究理事会;

关键词：

Malliavin calculus; maximum principle; stochastic control; mean-field type; jump diffusion; partial information; DIFFERENTIAL-EQUATIONS; PARTIAL INFORMATION; LEVY PROCESSES; PORTFOLIO;

D O I：

10.1080/17442508.2011.651619

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers a mean-field type stochastic control problem where the dynamics is governed by a controlled Ito-Levy process and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.

引用

页码：643 / 666

页数：24

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