Global closed-form approximation of free boundary for optimal investment stopping problems
File(s)
Accepted version
Author(s)
ma, jingtang
Xing, Jie
Zheng, harry
Type
Journal Article
Abstract
In this paper we study a utility maximization problem with both optimal control and opti-mal stopping in a finite time horizon. The value function can be characterized by a variationalequation that involves a free boundary problem of a fully nonlinear partial differential equation.Using the dual control method, we derive the asymptotic properties of the dual value functionand the associated dual free boundary for a class of utility functions, including power and non-HARA utilities. We construct a global closed-form approximation to the dual free boundary,which greatly reduces the computational cost. Using the duality relation, we find the approx-imate formulas for the optimal value function, trading strategy, and exercise boundary for theoptimal investment stopping problem. Numerical examples show the approximation is robust,accurate and fast.
Date Issued
2019-06-20
Date Acceptance
2019-04-09
Citation
SIAM Journal on Control and Optimization, 2019, 57 (3), pp.2092-2121
ISSN
0363-0129
Publisher
Society for Industrial and Applied Mathematics
Start Page
2092
End Page
2121
Journal / Book Title
SIAM Journal on Control and Optimization
Volume
57
Issue
3
Copyright Statement
© 2019, Society for Industrial and Applied Mathematics
Subjects
Science & Technology
Technology
Physical Sciences
Automation & Control Systems
Mathematics, Applied
Mathematics
optimal investment stopping problem
dual control method
free boundary
global closed-form approximation
CONVERGENCE
Industrial Engineering & Automation
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2019-06-20