A necessary and sufficient condition for absence of arbitrage with tame portfolios. (English) Zbl 0847.90016

Levental, Shlomo; Skorohod, Antolij V.

Ann. Appl. Probab. 5, No. 4, 906-925 (1995).

Summary: 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.

MSC:

91B28	Finance etc. (MSC2000)
60H30	Applications of stochastic analysis (to PDEs, etc.)

Keywords:

financial market; absence of arbitrage; tame portfolios; equivalent martingale measure; absence of approximate arbitrage