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2009 A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion
David Baker, Marc Yor
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Electron. J. Probab. 14: 1532-1540 (2009). DOI: 10.1214/EJP.v14-674

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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David Baker. Marc Yor. "A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion." Electron. J. Probab. 14 1532 - 1540, 2009. https://doi.org/10.1214/EJP.v14-674

Information

Accepted: 19 May 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1201.60033
MathSciNet: MR2519530
Digital Object Identifier: 10.1214/EJP.v14-674

Subjects:
Primary: 60G07
Secondary: 60G60

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