Viability and arbitrage under Knightian uncertainty
Apparaît également dans la collection : Advances in stochastic analysis for risk modeling / Avancées en analyse stochastique pour la modélisation des risques
We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original framework of Kreps ('79) and Harrison-Kreps ('79) to accommodate for Knightian Uncertainty: preferences of plausible agents are not necessarily determined by a single probability measure. The relations between arbitrage, viability, and existence of (non-)linear pricing rules are investigated. This is a joint work with Frank Riedel and Mete Soner.
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