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A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion
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David Baker, Université Pierre et Marie Curie
Marc Yor, Université Pierre et Marie Curie
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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.
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Full text: PDF
Pages: 1532-1540
Published on: July 4, 2009
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Electronic Journal of Probability. ISSN: 1083-6489 |
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