Annals of Finance

, Volume 2, Issue 1, pp 101–122 | Cite as

Stochastic equilibria for economies under uncertainty with intertemporal substitution

  • V. Filipe Martins-da-Rocha
  • Frank Riedel
Research Article


We consider the model of a stochastic pure exchange economy with a finite set of agents whose preferences exhibit local substitution in the sense of Hindy and Huang (1992). In order to prove the existence of Arrow–Debreu equilibria, it is assumed in Bank and Riedel (2001) that smooth subgradients exist (Assumption 1 in Bank and Riedel (2001)) and that they are uniformly bounded from above and away from zero (Assumption 2 in Bank and Riedel 2001).

In this paper, we prove that the existence of smooth subgradients implies local properness of preferences. By a slight improvement of classical existence results of the literature, we prove that the local properness of preferences is a sufficient condition for the existence of equilibria, rendering Assumption 2 in Bank and Riedel (2001) superfluous.


Stochastic pure exchange economies Intertemporal substitutability of consumption Arrow–Debreu equilibrium Local properness Optional random measures 

JEL Classification Numbers

D51 D91 


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.CeremadeUniversité Paris-DauphineParis Cedex 16France
  2. 2.Department of EconomicsRheinische Friedrich-Wilhelms-Universität BonnBonnGermany

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