Arbitrage and equilibrium in strategic security markets
In view of the fundamental price taking hypothesis, arbitrage is never compatible with equilibrium in Walrasian markets because the existence of an arbitrage opportunity in a competitive situation always leads to unbounded arbitrage activity. In strategic markets however, the mere effort of individuals to profit alters market clearing prices and thus distorts arbitrage opportunities as well. This observation suggests a different relationship between arbitrage and equilibrium, than in the competitive model. Indeed, we show that in such markets a spread between the cost of a portfolio and its returns is compatible with equilibrium. We provide an example of an equilibrium where a resourceless individual holds a portfolio with zero cost and positive return in every state. We further demonstrate via an asymptotic result, that no arbitrage is intimately related to price taking behaviour.