Optimal Control Problems Governed by MFSDEs with multi-defaults

Fuente: arXiv
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Autori principali: Gou, Zhun, Huang, Nan-jing, Wang, Ming-hui, Kang, Jian-hao
Natura: Preprint
Pubblicazione: 2020
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author Gou, Zhun
Huang, Nan-jing
Wang, Ming-hui
Kang, Jian-hao
author_facet Gou, Zhun
Huang, Nan-jing
Wang, Ming-hui
Kang, Jian-hao
contents In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.
format Preprint
id arxiv_https___arxiv_org_abs_2010_13608
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Optimal Control Problems Governed by MFSDEs with multi-defaults
Gou, Zhun
Huang, Nan-jing
Wang, Ming-hui
Kang, Jian-hao
Optimization and Control
60H07, 60H20, 60J76, 91G80, 93E20
In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.
title Optimal Control Problems Governed by MFSDEs with multi-defaults
topic Optimization and Control
60H07, 60H20, 60J76, 91G80, 93E20
url https://arxiv.org/abs/2010.13608