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November, 1995 A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios
Shlomo Levental, Antolii V. Skorohod
Ann. Appl. Probab. 5(4): 906-925 (November, 1995). DOI: 10.1214/aoap/1177004599

Abstract

We characterize absence of arbitrage with tame portfolios in the case of invertible volatility matrix. As a corollary we get that, under a certain condition, absence of arbitrage with tame portfolios is characterized by the existence of the so-called equivalent martingale measure. Without that condition, the existence of equivalent martingale measure is equivalent to absence of approximate arbitrage. The proofs are probabilistic and are based on a construction of two specific arbitrages. Some examples are provided.

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Shlomo Levental. Antolii V. Skorohod. "A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios." Ann. Appl. Probab. 5 (4) 906 - 925, November, 1995. https://doi.org/10.1214/aoap/1177004599

Information

Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0847.90016
MathSciNet: MR1384359
Digital Object Identifier: 10.1214/aoap/1177004599

Subjects:
Primary: 90A09
Secondary: 60H30

Keywords: Arbitrage , equivalent martingale measure , Girsanov formula , Martingale representation , portfolio

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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