Journal of Applied Probability

Stochastic boundary crossing probabilities for the Brownian motion

Xiaonan Che and Angelos Dassios

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Using martingale methods, we derive a set of theorems of boundary crossing probabilities for a Brownian motion with different kinds of stochastic boundaries, in particular compound Poisson process boundaries. We present both the numerical results and simulation experiments. The paper is motivated by limits on exposure of UK banks set by CHAPS. The central and participating banks are interested in the probability that the limits are exceeded. The problem can be reduced to the calculation of the boundary crossing probability from a Brownian motion with stochastic boundaries. Boundary crossing problems are also very popular in many fields of statistics.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 419-429.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 60G51: Processes with independent increments; Lévy processes

Boundary crossing probability first passage time probability Brownian motion


Che, Xiaonan; Dassios, Angelos. Stochastic boundary crossing probabilities for the Brownian motion. J. Appl. Probab. 50 (2013), no. 2, 419--429. doi:10.1239/jap/1371648950.

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