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.
"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