Global Closed-form Approximation of Free Boundary for Optimal Investment Stopping Problems

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Title: Global Closed-form Approximation of Free Boundary for Optimal Investment Stopping Problems
Authors: Ma, J
Xing, J
Zheng, H
Item Type: Journal Article
Abstract: n 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.
Issue Date: 1-Jan-2019
Date of Acceptance: 9-Apr-2019
ISSN: 0363-0129
Publisher: Society for Industrial and Applied Mathematics
Journal / Book Title: SIAM Journal on Control and Optimization
Copyright Statement: This paper is embargoed until publication.
Keywords: 0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Financial Mathematics

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