Optimal Stopping of a Brownian Excursion and an $\alpha$-dimensional Bessel Bridge

David Hobson; Jingfei Liu

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arXiv · 2504.19741

Optimal Stopping of a Brownian Excursion and an $\alpha$-dimensional Bessel Bridge

David Hobson·Jingfei Liu

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Abstract

We study the optimal stopping of an $\alpha$-dimensional Bessel bridge for the payoff $\phi(x)=x^n$, where $\alpha,n>0$. As a special case we consider the Brownian excursion with the identity function as the payoff ($\alpha=3,n=1$). For the Brownian excursion we can give an explicit solution but in the general case we provide a complete solution via a power series expansion.

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David Hobson, Jingfei Liu. 2025-04-28. Optimal Stopping of a Brownian Excursion and an $\alpha$-dimensional Bessel Bridge. https://arxiv.org/abs/2504.19741

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