Approximations of boundary crossing probabilities for a Brownian motion

Alex Novikov; Volf Frishling; Nino Kordzakhia

Approximations of boundary crossing probabilities for a Brownian motion

Alex Novikov^*, Volf Frishling, Nino Kordzakhia

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

77 Citations (Scopus)

Abstract

Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

Original language	English
Pages (from-to)	1019-1030
Number of pages	12
Journal	Journal of Applied Probability
Volume	36
Issue number	4
Publication status	Published - Dec 1999
Externally published	Yes

Keywords

First passage times
Girsanov transformation
Numerical integration
Werner process

Cite this

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title = "Approximations of boundary crossing probabilities for a Brownian motion",

abstract = "Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.",

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author = "Alex Novikov and Volf Frishling and Nino Kordzakhia",

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T1 - Approximations of boundary crossing probabilities for a Brownian motion

AU - Novikov, Alex

AU - Frishling, Volf

AU - Kordzakhia, Nino

PY - 1999/12

Y1 - 1999/12

N2 - Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

AB - Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

KW - First passage times

KW - Girsanov transformation

KW - Numerical integration

KW - Werner process

UR - https://www.scopus.com/pages/publications/0033426760

M3 - Article

AN - SCOPUS:0033426760

SN - 0021-9002

VL - 36

SP - 1019

EP - 1030

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 4

ER -

Approximations of boundary crossing probabilities for a Brownian motion

Abstract

Keywords

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