Refinements to the generic existence of equilibrium in incomplete markets

Lionel Boisdeffre
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Lionel Boisdeffre: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: The paper demonstrates the generic existence of general equilibria in incomplete markets with well behaved price properties. The economy has two periods and an ex ante uncertainty over the state of nature to be revealed at the second period. Securities pay off in cash or commodities at the second period, conditionally on the state of nature to be revealed. They permit financial transfers across periods and states, which are insufficient to span all state contingent claims to value, whatever the spot price to prevail. Under smooth preference and the standard Radner (1972) perfect foresight assumptions, equilibrium is shown to exist, except for a closed set of measure zero of endowments and securities. The proof provides additional arguments and insights to Duffie-Shafer's (1985) on the same subject and refines it in two ways. First, equilibrium in shown to exist generically for any norm values of commodity prices on any spot market, and for any collection of state prices. Second, assets need no longer pay off in commodities, but may in any mix of cash and goods.

Keywords: sequential equilibrium; temporary equilibrium; perfect foresight; existence; rational expectations; financial markets; asymmetric information; arbitrage; équilibre séquentiel; équilibre temporaire; anticipations parfaites; existence de l'équilibre; anticipations rarionnelles; marchés incomplets; asymétrie d'information (search for similar items in EconPapers)
Date: 2019-06
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Published in 2019

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