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Market Selection and the Absence of Arbitrage

A central conjecture of behavioural finance is that arbitrage opportunities appear as a result of systematic irrational investment behaviour and persist since real-world arbitrage trades actually involve costs and risks due to market frictions and non-fundamental risk. This paper shows that the no-arbitrage condition can emerge from the market selection process even if systematic irrational trading behaviour occurs permanently and there are no strategic arbitrage trades. The model consists of two types of agents and two assets. Dividends are independently and identically distributed over time. Both types of agents invest positive amounts of wealth into each asset and keep portfolio weights constant. Arbitrage opportunities naturally occur in the short and medium term depending on how both types invest but disappear in the long run if both types survive the market selection process - regardless of both types' portfolios and initial wealth distribution. A necessary condition for arbitrage opportunities to persist is that one type of agents drives the other one out of the market.