Stochastic maximum principle for optimal liquidation with control-dependent terminal time
File(s)
Author(s)
Cesari, Riccardo
Zheng, harry
Type
Journal Article
Abstract
In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum principle (SMP) which is markedly different in its Hamiltonian condition from that of the standard SMP with fixed terminal time. We present a simple example in which the optimal solution satisfies the SMP in this paper but fails the standard SMP in the literature.
Date Issued
2022-05-10
Date Acceptance
2021-09-28
Citation
Applied Mathematics and Optimization, 2022, 85 (43), pp.1-32
ISSN
0095-4616
Publisher
Springer
Start Page
1
End Page
32
Journal / Book Title
Applied Mathematics and Optimization
Volume
85
Issue
43
Copyright Statement
© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://link.springer.com/article/10.1007/s00245-022-09848-1
Grant Number
EP/V008331/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Stochastic maximum principle
Control-dependent terminal time
Optimal liquidation
Variational analysis
Backwards stochastic differential equations
EQUATIONS
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2022-05-10