Optimal stopping of an $\alpha$-Brownian bridge

TL;DR

This paper investigates the optimal stopping problem for an alpha-Brownian bridge, extending previous work on the standard Brownian bridge, and explores the behavior as alpha approaches zero.

Contribution

It generalizes the optimal stopping problem from the Brownian bridge to the alpha-Brownian bridge and analyzes the behavior for small alpha values.

Findings

Extended the optimal stopping framework to alpha-Brownian bridges

Analyzed the behavior of the process as alpha approaches zero

Provided insights into the stopping strategies for different alpha values

Abstract

We study the problem of stopping an $\alpha$-Brownian bridge as close as possible to its global maximum. This extends earlier results found for the Brownian bridge (the case $\alpha=1$). The exact behavior for $\alpha$ close to $0$ is investigated.