Optimal stopping of Gauss-Markov bridges

TL;DR

This paper addresses the finite-horizon optimal stopping problem for Gauss-Markov bridges, providing a transformation approach, proving boundary regularity, and illustrating numerical methods for boundary computation.

Contribution

It introduces a novel transformation method for solving the problem and characterizes the optimal stopping boundary via an integral equation.

Findings

Optimal stopping boundary is Lipschitz continuous away from the horizon.

Boundary characterized by a unique integral equation solution.

Numerical algorithm effectively computes the boundary in examples.

Abstract

We solve the non-discounted, finite-horizon optimal stopping problem of a Gauss-Markov bridge by using a time-space transformation approach. The associated optimal stopping boundary is proved to be Lipschitz continuous on any closed interval that excludes the horizon, and it is characterized by the unique solution of an integral equation. A Picard iteration algorithm is discussed and implemented to exemplify the numerical computation and geometry of the optimal stopping boundary for some illustrative cases.