A simple integral equation approach for optimal investment stopping problems with partial information
Author(s)
Xing, Jie
Ma, Jingtang
Zheng, Harry
Type
Journal Article
Abstract
In this paper, we study a finite horizon optimal investment stopping problem with an unobservable random variable for the return of a risky asset. Using the Bayesian filter and the dual control approach, we transform the original primal problem into a dual finite horizon optimal stopping problem, which results in the dual value function satisfying a variational inequality with two state variables. For a class of utility functions that includes power utility and non–hyperbolic absolute risk aversion utility, we show that the free boundary satisfies a Volterra-type nonlinear integral equation with expectation over the joint distribution of the dual state process and the filtered probability process, and we simplify and solve the integral equation with the dimension reduction and backward recursive methods. We also construct two simple closed-form approximations for the free boundary using its asymptotic properties and show their accuracy and efficiency with numerical examples. Furthermore, we demonstrate that different model parameters may lead to one, two, or no free boundaries with a simple example.
Date Issued
2026-02-01
Date Acceptance
2025-01-25
Citation
Mathematics of Operations Research, 2026, 51 (1), pp.542-567
ISSN
0364-765X
Publisher
Institute for Operations Research and Management Sciences
Start Page
542
End Page
567
Journal / Book Title
Mathematics of Operations Research
Volume
51
Issue
1
Copyright Statement
© 2025, INFORMS. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
Publication Status
Published
Date Publish Online
2025-02-28