Baker, David; Yor, Marc A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. (English) Zbl 1201.60033 Electron. J. Probab. 14, 1532-1540 (2009). Summary: 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 A. G. Starling, J. B. Klerlein, J. Kier and E. C. Carr [Congr. Numerantium 162, 129–137 (2003; Zbl 1056.05088)] 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. Cited in 10 Documents MSC: 60G07 General theory of stochastic processes 60G60 Random fields 60G44 Martingales with continuous parameter 60J65 Brownian motion Keywords:convex order; Brownian sheet; asian option; running average Citations:Zbl 1056.05088 PDF BibTeX XML Cite \textit{D. Baker} and \textit{M. Yor}, Electron. J. Probab. 14, 1532--1540 (2009; Zbl 1201.60033) Full Text: DOI EuDML EMIS