The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 4 (1995), 906-925.
A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios
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.
Ann. Appl. Probab., Volume 5, Number 4 (1995), 906-925.
First available in Project Euclid: 19 April 2007
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Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
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