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Boundary crossing probability for Brownian motion and general boundaries

Published online by Cambridge University Press:  14 July 2016

Liqun Wang*
Affiliation:
University of Basel
Klaus Pötzelberger*
Affiliation:
University of Economics and Business Administration Vienna
*
Postal address: Institute for Statistics and Econometrics, University of Basel, Holbeinstrasse 12, CH-4051 Basel, Switzerland.
∗∗Postal address: Institute of Statistics, University of Economics and Business Administration Vienna, Augasse 2–6, A-1090 Vienna, Austria.

Abstract

An explicit formula for the probability that a Brownian motion crosses a piecewise linear boundary in a finite time interval is derived. This formula is used to obtain approximations to the crossing probabilities for general boundaries which are the uniform limits of piecewise linear functions. The rules for assessing the accuracies of the approximations are given. The calculations of the crossing probabilities are easily carried out through Monte Carlo methods. Some numerical examples are provided.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1997 

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