journal of economic theory 71, 313323 (1996) The Survival Assumption and Existence of Competitive Equilibria When Asset Markets are Incomplete* Piero Gottardi Dipartimento di Scienze Economiche, Universita di Venezia, 30123 Venezia, Italy; and Department of Economics, Harvard University, Cambridge, Massachusetts 02138 and Thorsten Hens Wirtschaftstheorie II, University of Bonn, Lenne strasse 37, D-53113 Bonn, Germany Received July 20, 1994; revised December 14, 1995 The paper studies the role and the formulation of the survival assumption with incomplete markets. We are able to show the existence of a competitive equilibrium when the agents' endowments lie on the boundary of their consumption set. However, for this some additional assumptions with respect to the complete market case are needed. These are joint restrictions on the asset structure and the distribu- tion of the endowments and preferences. Journal of Economic Literature Classifica- tion Numbers: D52, C62, G10.  1996 Academic Press, Inc. 1. INTRODUCTION The condition that every agent's endowment lies in the interior of his consumption set is clearly a very restrictive assumption in a general equi- librium model, especially if commodities are dated and distinguished by states of the world. As is well known from Arrow's [1] exceptional case, boundary endowments may cause a lack of existence of competitive equilibria. The problem is that a quasi-equilibrium may fail to be an equi- librium if a survival condition is not satisfied (Debreu [5]). However, if preferences are strictly monotone, with complete markets such a condition article no. 0123 313 0022-053196 18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved. * We wish to thank P. Hammond, P. Klinger-Monteiro, H. Polemarchakis, J. Werner, and an anonymous referee for valuable comments. Financial support by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn, by Trinity College, Cambridge, and by CNR at the University of Venice is gratefully acknowledged.