Sperner's lemma and competitive equilibrium with incomplete financial markets *

Thanh Le (1) , Cuong Le Van (2, 3) , Ngoc-Sang Pham (4) , Cagri Saglam (5)

1 University of Wollongong [Australia]
2 CNRS - Centre National de la Recherche Scientifique
3 PSE - Paris School of Economics
4 Métis Lab EM Normandie
5 Bilkent University [Ankara]

We establish the existence of a competitive equilibrium in a two-period stochastic economy with incomplete financial markets by using Sperner’s lemma. Our existence result covers (but is not limited to) several results in the literature, including the cases of nominal and numéraire assets. Moreover, there may exist a continuum of equilibrium prices.

Mots clés: Sperner's lemma; fixed-point theorem; general equilibrium; incomplete market; indeterminacy

Domaines: Economies et finances; Mathématiques [math]

Thanh Le, Cuong Le Van, Ngoc-Sang Pham, Cagri Saglam. Sperner's lemma and competitive equilibrium with incomplete financial markets *. Economics Letters, In press. ⟨hal-04552148⟩