On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function

Tristan Guillaume

Journal of Probability and Statistics, 2015, vol. 2015, 1-22

Abstract:

This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:391681

DOI: 10.1155/2015/391681

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