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arXiv · 2504.19741

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

David Hobson·Jingfei Liu
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Abstract

We study the optimal stopping of an $α$-dimensional Bessel bridge for the payoff $ϕ(x)=x^n$, where $α,n>0$. As a special case we consider the Brownian excursion with the identity function as the payoff ($α=3,n=1$). 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 $α$-dimensional Bessel Bridge. https://arxiv.org/abs/2504.19741

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