Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss

Abstract

Based on a concept of asymptotic exponential arbitrage proposed by Follmer-Schachermayer, the author introduces a new formulation of asymptotic arbitrage with two main differences from the previous one: Firstly, the realising strategy does not depend on the maturity time while the previous one does, and secondly, the probable maximum loss is allowed to be small constant instead of a decreasing function of time. The main result gives a sufficient condition on stock prices for the existence of such asymptotic arbitrage. As a consequence, she gives a new proof of a conjecture of Follmer and Schachermayer.