Existence of financial equilibria with restricted participation

Zaier Aouani (1) , Bernard Cornet (2, 3, 4)

1 ISET
2 CES - Centre d'économie de la Sorbonne
3 Department of economics, University of Kansas
4 PSE - Paris School of Economics

We consider a two-date model of a financial exchange economy with finitely many agents having nonordered preferences and portfolio constraints. There is a market for physical commodities at any state today or tomorrow and financial transfers across time and across states are allowed by means of finitely many nominal assets or numéraire assets. We prove a general existence result of equilibria for such a financial exchange economy in which portfolios are defined by linear constraints, extending the framework of linear equality constraints by Balasko et al. (1990), and the existence results in the unconstrained case by Cass (1984, 2006), Werner (1985), Duffie (1987), and Geanakoplos and Polemarchakis (1986). Our main result is a consequence of an auxiliary result, also of interest for itself, in which agents' portfolio constraints are defined by general closed convex sets and the financial structure is assumed to satisfy a "nonredundancy-type" assumption, weaker than the ones in Radner (1972) and Siconolfi (1989).

Mots clés: Restricted participation; Portfolio constraints; Financial exchange economy; Equilibrium; Existence; Arbitrage-free asset prices

Domaines: Economies et finances

Zaier Aouani, Bernard Cornet. Existence of financial equilibria with restricted participation. Journal of Mathematical Economics, 2009, 45 (12), pp.772-786. ⟨10.1016/j.jmateco.2009.10.001⟩. ⟨hal-00629748⟩