Moment generating function of the reciprocal of an integral of geometric Brownian motion
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- by Kyounghee Kim PDF
- Proc. Amer. Math. Soc. 132 (2004), 2753-2759 Request permission
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.References
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Additional Information
- Kyounghee Kim
- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
- Email: kkim26@syr.edu
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2054802