Arbitrage and Equilibrium with Portfolio Constraints

URL des Documents de travailDocuments de travail du Centre d'Economie de la Sorbonne 2009.77 - ISSN : 1955-611XWe consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent's portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (1989). Using an approach that dates back to Cass (1984, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are aloso quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduce that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent's portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (2005).Dans un modèle d'économie financière avec des contraintes exogènes sur les portefeuilles des agents, nous proposons une généralisation du résultat de Cass (1984, 2006) qui exhibe une classe de prix des actifs nominaux sans opportunité d'arbitrage qui sont des équilibres ou des quasi-équilibres de l'économie. Ce résultat étend des travaux précédents de Martins-da-Rocha et Triki (2005)