DUALITY AND GENERAL EQUILIBRIUM THEORY UNDER KNIGHTIAN UNCERTAINTY *

Patrick Beissner 1 Laurent Denis 2
2 Laboratoire Manceau de Mathématiques
LMM - Laboratoire Manceau de Mathématiques
Abstract : Any dynamic or stochastic notion of a general equilibrium relies on the underlying commodity space. Under sole risk and without multiple–prior uncertainty the usual choice is a Lebesgue space from standard measure theory. In the case of volatility uncertainty it turns out that such a type of function space is no longer appropriate. For this reason we introduce and discuss a new natural commodity space, which can be constructed in three independent and equivalent ways. Each approach departs from one possible way to construct Lebesgue spaces. Moreover, we give a complete representation of the resulting topological dual space. This extends the classic Riesz representation in a natural way. Elements therein are the candidates for a linear equilibrium price system. This representation result has direct implications for the microeconomic foundation of finance under Knightian uncertainty.
Type de document :
Pré-publication, Document de travail
2017
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Dernière modification le : lundi 20 novembre 2017 - 15:08:44

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Patrick Beissner, Laurent Denis. DUALITY AND GENERAL EQUILIBRIUM THEORY UNDER KNIGHTIAN UNCERTAINTY *. 2017. 〈hal-01585973〉

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