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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 52 open journal systems 


A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion

David Baker, Université Pierre et Marie Curie
Marc Yor, Université Pierre et Marie Curie


Abstract
We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion.This provides a short proof of the recent result due to P. Carr et al that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion is replaced by a stable subordinator.


Full text: PDF

Pages: 1532-1540

Published on: July 4, 2009


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Electronic Journal of Probability. ISSN: 1083-6489