Arbitrage in stationary markets

We analyse questions of arbitrage in financial markets in which asset prices change in time as stationary stochastic processes. The main focus of the paper is on a model where the price vectors are independent and identically distributed. In the framework of this model, we find conditions that are necessary and sufficient for the absence of arbitrage opportunities. We discuss the relations between the results obtained and the phenomenon of “volatility-induced growth” in stationary markets. Financial support by the Swiss National Center of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged.