Excess profit relative to the benchmark asset under the $ \alpha $-confidence level

We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ \alpha $-confidence level, $ \alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ \alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ \alpha $-REP.