Arbitrage Opportunities in Diverse Markets via a Non-equivalent Measure Change

We study arbitrage opportunities in diverse markets as introduced by Fernholz (J Math Econ 31:393–417, 1999). By a change of measure technique we are able to generate a variety of diverse markets. The construction is based on an absolutely continuous but non-equivalent measure change which implies the existence of instantaneous arbitrage opportunities in diverse markets. For this technique to work, we single out a crucial non-degeneracy condition. Moreover, we discuss the dynamics of the price process under the new measure as well as further applications.Both authors gratefully acknowledge financial support by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK). The NCCR FINRISK is a research program supported by the Swiss National Science Foundation. The first author also thanks Credit Suisse Group for financial support.