Arbitrage and control problems in finance: A presentation

When the markets are dynamically complete and without imperfections there are three equivalent approaches in order to price a given asset : the arbitrage approach through the existence of a risk-neutral density, the utility approach through a utility maximization program and the equilibrium approach through the market clearing conditions. When there are imperfections these three approaches lead to different results. This special issue explores these three approaches and their possible links. In this introduction we present an overview of the main contributions in this field as well as the main techniques and results. In particular, we introduce the other papers of this issue and we compare them quickly to the existing literature.