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June 2013 On the uniqueness of martingales with certain prescribed marginals
Michael R. Tehranchi
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J. Appl. Probab. 50(2): 557-575 (June 2013). DOI: 10.1239/jap/1371648961

Abstract

This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S0eσ X2X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Black-Scholes model with volatility σ>0.) Then there exists a Brownian motion W such that Xt=Wt+o(t1/4+ ε) as t↑∞ for any ε> 0.

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Michael R. Tehranchi. "On the uniqueness of martingales with certain prescribed marginals." J. Appl. Probab. 50 (2) 557 - 575, June 2013. https://doi.org/10.1239/jap/1371648961

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1291.60084
MathSciNet: MR3102500
Digital Object Identifier: 10.1239/jap/1371648961

Subjects:
Primary: 60G42, 60G44, 91B25

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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