Patrik Albin
Mathematical Sciences, Chalmers and Göteborg University

On the existence of non-Brownian motion martingales with Brownian motion univariate marginal distributions

Abstract

We give a rather complete dicussion, including own results as well 
as references to the literature, of the issue whether there exists 
a martingale that have the same univariate marginal distributions as 
a Brownian motion but is not a Brownian motion.

Besides constituting an argubly interesting theoretical problem with 
an argubly beautiful solution, this issue is of practical interest in 
mathematical finance, simply to find alternatives to the traditional 
Black-Scholes model based on Brownian motion.

The problem was suggested to us by Fima C Klebaner.