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{1177004599,
author = {Levental, Shlomo and Skorohod, Antolii V.},
title = {A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios},
journal = {Ann. Appl. Probab.},
volume = {5},
number = {4},
year = {1995},
pages = { 906-925},
language = {en},
url = {http://dml.mathdoc.fr/item/1177004599}
}
Levental, Shlomo; Skorohod, Antolii V. A Necessary and Sufficient Condition for Absence of Arbitrage with Tame Portfolios. Ann. Appl. Probab., Tome 5 (1995) no. 4, pp. 906-925. http://gdmltest.u-ga.fr/item/1177004599/