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Licensed Unlicensed Requires Authentication Published by De Gruyter January 30, 2019

Sensitivity of boundary crossing probabilities of the Brownian motion

  • Sercan Gür EMAIL logo and Klaus Pötzelberger

Abstract

The paper analyzes the sensitivity of boundary crossing probabilities of the Brownian motion to perturbations of the boundary. The first- and second-order sensitivities, i.e. the directional derivatives of the probability, are derived. Except in cases where boundary crossing probabilities for the Brownian bridge are given in closed form, the sensitivities have to be computed numerically. We propose an efficient Monte Carlo procedure.

References

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Received: 2018-06-29
Revised: 2018-12-12
Accepted: 2019-01-21
Published Online: 2019-01-30
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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