Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

Qingxin Meng; Yang Shen

doi:10.1016/j.cam.2014.10.011

Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

Qingxin Meng, Yang Shen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

53 Citations (Scopus)

Abstract

This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

Original language	English
Pages (from-to)	13-30
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	279
DOIs	https://doi.org/10.1016/j.cam.2014.10.011
Publication status	Published - 1 May 2015
Externally published	Yes

Keywords

Advanced backward stochastic differential equation
Mean-field
Optimal control
Stochastic delay differential equation
Stochastic maximum principle

Access to Document

10.1016/j.cam.2014.10.011

Cite this

@article{685d842b4265458bbd2cbae624ac7775,

title = "Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach",

abstract = "This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.",

keywords = "Advanced backward stochastic differential equation, Mean-field, Optimal control, Stochastic delay differential equation, Stochastic maximum principle",

author = "Qingxin Meng and Yang Shen",

year = "2015",

month = may,

day = "1",

doi = "10.1016/j.cam.2014.10.011",

language = "English",

volume = "279",

pages = "13--30",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

}

TY - JOUR

T1 - Optimal control of mean-field jump-diffusion systems with delay

T2 - A stochastic maximum principle approach

AU - Meng, Qingxin

AU - Shen, Yang

PY - 2015/5/1

Y1 - 2015/5/1

N2 - This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

AB - This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles.

KW - Advanced backward stochastic differential equation

KW - Mean-field

KW - Optimal control

KW - Stochastic delay differential equation

KW - Stochastic maximum principle

UR - http://www.scopus.com/inward/record.url?scp=84910602890&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2014.10.011

DO - 10.1016/j.cam.2014.10.011

M3 - Article

SN - 0377-0427

VL - 279

SP - 13

EP - 30

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this