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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Moment generating function of the reciprocal of an integral of geometric Brownian motion


Author: Kyounghee Kim
Journal: Proc. Amer. Math. Soc. 132 (2004), 2753-2759
MSC (2000): Primary 60J65; Secondary 60G35
DOI: https://doi.org/10.1090/S0002-9939-04-07449-0
Published electronically: April 21, 2004
MathSciNet review: 2054802
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Abstract: In this paper we obtain a simple, explicit integral form for the moment generating function of the reciprocal of the random variable defined by $A^{(\nu )}_t := \int ^t _0 \exp (2B_s + 2 \nu s) ds$, where $B_s$, $s>0$, is a one-dimensional Brownian motion starting from 0. In case $\nu = 1$, the moment generating function has a particularly simple form.


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Additional Information

Kyounghee Kim
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: kkim26@syr.edu

Keywords: Geometric Brownian motion, Asian options, moment generating functions
Received by editor(s): December 13, 2002
Received by editor(s) in revised form: July 18, 2003
Published electronically: April 21, 2004
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2004 American Mathematical Society