On first exit times and their means for Brownian bridges.

Christel Geiss, Antti Luoto, Paavo Salminen

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    For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), ,, h>0,$ behaves as $O(h^2)$ when $h downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimateneeded by Walsh to determine the convergence of the binomial tree scheme for European options.

    Original languageUndefined/Unknown
    Pages (from-to)701–722
    JournalJournal of Applied Probability
    Issue number3
    Publication statusPublished - 2019
    MoE publication typeA1 Journal article-refereed

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