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Optimal Stopping of a Brownian Excursion and an $α$-dimensional Bessel Bridge
David Hobson, Jingfei Liu · 2025-04-28 · via math.PR updates on arXiv.org

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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