Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon

A.J.E.M. Janssen; J.S.H. Leeuwaarden, van

Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon

A.J.E.M. Janssen, J.S.H. Leeuwaarden, van

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Abstract

A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function.

Original language	English
Place of Publication	Eindhoven
Publisher	Eurandom
Number of pages	8
Publication status	Published - 2008

Publication series

Name	Report Eurandom
Volume	2008054
ISSN (Print)	1389-2355

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abstract = "A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function.",

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Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon

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