Optimal Trading of Arbitrage Opportunities with Market Impact

Abstract

This paper studies the optimal trading strategy of arbitrageurs in a dynamic economy where there are transaction costs and the arbitrageur’s trades reduce (or eliminate) future arbitrage opportunities. In contrast to the standard textbook arbitrage trading strategy which has infinite present value, we show that an arbitrageur’s expected discounted trading profits are finite. In addition, we show that it is rational for arbitrageurs not to trade the first time that arbitrage profits exceed their transaction costs. In fact, in our economy, arbitrage profits will often exceed the transaction cost band, disappear, then reappear again. The implications of this observation for the existing empirical literature testing for arbitrage opportunities is also discussed.