Arbitrage and equilibrium with portfolio constraints
Résumé
We 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 (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384-405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also 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 deduces 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 (Working Paper, University of Paris 1, 2005).