Sperner’s lemma and competitive equilibrium with incomplete financial markets

• Published in: Economics letters Vol. 238; p. 111720
• Main Authors: Le, Thanh, Le Van, Cuong, Pham, Ngoc-Sang, Sağlam, Çağrı
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-05-2024; Elsevier
• Subjects: Economics and Finance; Fixed-point theorem; General equilibrium; Humanities and Social Sciences; Incomplete market; Indeterminacy; Mathematics; Sperner’s lemma; Sperner’s lemma; D5; Fixed-point theorem; Incomplete market; G1; C60; Indeterminacy; C62; General equilibrium; fixed-point theorem; Sperner's lemma; general equilibrium; incomplete market; indeterminacy
• ISSN: 0165-1765
• DOI: 10.1016/j.econlet.2024.111720

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.
•By using Sperner’s lemma, we establish the existence of competitive equilibrium in a two-period stochastic economy with incomplete financial markets.•Asset price is a convex combination of the return matrix with exogenous weights.•Our existence result covers several results in the literature, on nominal and numéraire assets.