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A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. (English) Zbl 1201.60033

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.

MSC:

60G07 General theory of stochastic processes
60G60 Random fields
60G44 Martingales with continuous parameter
60J65 Brownian motion

Citations:

Zbl 1056.05088
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