Existence of Equilibrium in Finite Dimensional Asset Markets

Thai Ha-Huy (1) , Cuong Le Van (2, 3) , Myrna Wooders (4)

1 EPEE - Centre d'Etudes des Politiques Economiques
2 IPAG Business School
3 PSE - Paris School of Economics
4 Vanderbilt University [Nashville]

We consider a pure exchange asset model with a finite number of agents and a finite number of states of nature where short sells are allowed. We present the definition of weak no-arbitrage price, a weaker notion of noarbitrage price than the one of Werner, and prove that if the utility functions satisfy the maximal and closed gradients conditions we propose in this paper, then there exists an equivalence between existence of a general equilibrium and existence of a price which is weak no-arbitrage price for all the agents.

Keywords: asset market equilibrium; individually rational attainable allocations; individually rational utility set; no-arbitrage prices; no-arbitrage condition

Domains: Quantitative Finance [q-fin]

Thai Ha-Huy, Cuong Le Van, Myrna Wooders. Existence of Equilibrium in Finite Dimensional Asset Markets. 2024. ⟨hal-04131008v2⟩