STOCHASTIC MAXIMUM PRINCIPLE FOR FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SUBDIFFUSION

被引：0

作者：

Zhang, Shuaiqi ^{[1
]}

Chen, Zhen-qing ^{[2
]}

机构：

[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 05期

基金：

中国国家自然科学基金;

关键词：

stochastic control; stochastic maximum principle; forward-backward stochastic differential equation; anomalous sub diffusion; RANDOM-WALKS;

D O I：

10.1137/23M1620168

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study optimal stochastic control problems for fully coupled forward-backward stochastic differential equations driven by anomalous sub diffusion, which have nontrivial mixed features of deterministic and stochastic controls. Both the stochastic maximum principle (SMP) and sufficient SMP are obtained by using a convex variational method. The paper ends with an application of the main results of this paper to a linear quadratic problem in the subdiffusive setting, which is solved explicitly.

引用

页码：2433 / 2455

页数：23

共 23 条

[1] NECESSARY AND SUFFICIENT CONDITIONS OF OPTIMALITY FOR OPTIMAL CONTROL PROBLEMS OF FORWARD AND BACKWARD SYSTEMS
Bahlali, S.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2010, 54 (04) : 553 - 570
[2] RISK, AMBIGUITY, AND THE SAVAGE AXIOMS
ELLSBERG, D
[J]. QUARTERLY JOURNAL OF ECONOMICS, 1961, 75 (04) : 643 - 669
[3] Ikeda N., 1989, Stochastic Differential Equations and Diffusion Processes, V24
[4] Ma J, 2007, LECT NOTES MATH, V1702, P1, DOI 10.1007/978-3-540-48831-6
[5] Limit theorems for continuous-time random walks with infinite mean waiting times
Meerschaert, MM
Scheffler, HP
[J]. JOURNAL OF APPLIED PROBABILITY, 2004, 41 (03) : 623 - 638
[6] The random walk's guide to anomalous diffusion: a fractional dynamics approach
Metzler, R
Klafter, J
[J]. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2000, 339 (01): : 1 - 77
[7] A TIME-CHANGED STOCHASTIC CONTROL PROBLEM AND ITS MAXIMUM PRINCIPLE
Nane, Erkan
Ni, Yinan
[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2021, 41 (02): : 193 - 215
[8] MAXIMUM PRINCIPLES FOR OPTIMAL CONTROL OF FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS
Oksendal, Bernt
Sulem, Agnes
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (05) : 2945 - 2976
[9] BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS AND APPLICATIONS TO OPTIMAL-CONTROL
PENG, SG
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 1993, 27 (02) : 125 - 144
[10] Fully coupled forward-backward stochastic differential equations and applications to optimal control
Peng, SG
Wu, Z
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (03) : 825 - 843

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