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

2025/04/28 by David Hobson, Hobson, David, J. Frank Liu +1
Business, Management and Accounting · Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Queuing Theory Analysis #Bessel function #Bessel process #Brownian bridge #Brownian excursion #Brownian motion #Excursion #FOS: Mathematics #Power series #Probability (math.PR) #Series (stratigraphy) #Stochastic processes and financial applications #stochastic dynamics and bifurcation

paper · doi:10.48550/arxiv.2504.19741

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the optimal stopping of an α-dimensional Bessel bridge for the payoff ϕ(x)=xⁿ, 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.

Citations

• Optimally Stopping a Brownian Bridge with an Unknown Pinning Time: A Bayesian Approach
• Optimal double stopping of a Brownian bridge

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