A Simple Integral Equation Approach for Optimal Investment Stopping Problems with Partial Information.

This article investigates a finite-horizon optimal investment stopping problem where the drift (return) of a risky asset is an unobservable random variable. Employing Bayesian filtering and a dual control approach, the authors transform the original problem into a two-dimensional dual optimal stopping problem characterized by a variational inequality with two state variables. For a broad class of utility functions—including power utility and non-hyperbolic absolute risk aversion (non-HARA) utility—they prove the existence and uniqueness of a continuous free boundary that separates continuation and stopping regions, and show this boundary satisfies a Volterra-type nonlinear integral equation. To address computational challenges, they apply dimension reduction and backward recursion methods to simplify and solve the integral equation, and propose two global closed-form approximations for the free boundary, demonstrating their accuracy through numerical examples. The paper also analyzes how model parameters influence the number and existence of free boundaries, providing examples where one, two, or no free boundaries arise, and discusses limitations of extending the approach to models with hidden Markov chain drifts.