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Stochastic Boundary Crossing Probabilities for the Brownian Motion

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  30 January 2018

Xiaonan Che  and
Angelos Dassios
Xiaonan Che*
Affiliation:
London School of Economics and Political Science
Angelos Dassios*
Affiliation:
London School of Economics and Political Science
*
∗ Postal address: Department of Statistics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, UK.
∗ Postal address: Department of Statistics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, UK.
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Abstract

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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.

Keywords

Boundary crossing probabilityfirst passage time probabilityBrownian motion

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 419 - 429
Copyright
© Applied Probability Trust 

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