The Annals of Applied Probability

A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios

Shlomo Levental and Antolii V. Skorohod

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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.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 4 (1995), 906-925.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004599

Digital Object Identifier
doi:10.1214/aoap/1177004599

Mathematical Reviews number (MathSciNet)
MR1384359

Zentralblatt MATH identifier
0847.90016

JSTOR
links.jstor.org

Subjects
Primary: 90A09
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Martingale representation Girsanov formula arbitrage portfolio equivalent martingale measure

Citation

Levental, Shlomo; Skorohod, Antolii V. A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios. Ann. Appl. Probab. 5 (1995), no. 4, 906--925. doi:10.1214/aoap/1177004599. https://projecteuclid.org/euclid.aoap/1177004599


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