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Stochastic equilibria for economies under uncertainty with intertemporal substitution

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Abstract

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.

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Authors and Affiliations

  1. Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    V. Filipe Martins-da-Rocha

  2. Department of Economics, Rheinische Friedrich-Wilhelms-Universität Bonn, Adenauerallee 24-26, 53113, Bonn, Germany

    Frank Riedel

Authors
  1. V. Filipe Martins-da-Rocha
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  2. Frank Riedel
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Correspondence to V. Filipe Martins-da-Rocha.

Additional information

This work was partially done while F. Riedel was visiting Ceremade at Université Paris–Dauphine

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Martins-da-Rocha, V.F., Riedel, F. Stochastic equilibria for economies under uncertainty with intertemporal substitution. Annals of Finance 2, 101–122 (2006). https://doi.org/10.1007/s10436-005-0025-8

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  • DOI: https://doi.org/10.1007/s10436-005-0025-8

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