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Existence and uniqueness of Arrow-Debreu equilibria with consumptions in $\mathbf{L}^0_+$

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  • Dmitry Kramkov

Abstract

We consider an economy where agents' consumption sets are given by the cone $\mathbf{L}^0_+$ of non-negative measurable functions and whose preferences are defined by additive utilities satisfying the Inada conditions. We extend to this setting the results in \citet{Dana:93} on the existence and uniqueness of Arrow-Debreu equilibria. In the case of existence, our conditions are necessary and sufficient.

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  • Dmitry Kramkov, 2013. "Existence and uniqueness of Arrow-Debreu equilibria with consumptions in $\mathbf{L}^0_+$," Papers 1304.3284, arXiv.org, revised May 2013.
    • Handle: RePEc:arx:papers:1304.3284
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    Cited by:

    1. Dmitry Kramkov, 2015. "Existence of an endogenously complete equilibrium driven by a diffusion," Finance and Stochastics, Springer, vol. 19(1), pages 1-22, January.

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