Research

Published papers  

1. "Arbitrage and equilibrium in economies with short-selling and ambiguity" with Thai Ha-Huy and Cuong Le Van  (Journal of Mathematical Economics, 2018) 

Abstract: We consider a model with a finite number of states of nature where short sells are allowed. We present a notion of no-arbitrage price weaker than the one of Werner (1987) that we call weak no-arbitrage price. We prove that in the case of maximin expected utility functions, the existence of one common weak no-arbitrage price is equivalent to the existence of an equilibrium.  

Working papers 

2. The existence of equilibrium in incomplete markets with a countable number of states with Jean-Marc Bonissseau and Cuong Le Van

Abstract: We consider a simple two-period economy $\grave{a}$ la Hart with either finitely or infinitely countable many states of nature. The first part of the results deals with the existence of financial equilibrium with finite number of states. In this case, we give a simpler proof for the existence result than the one's Florenzano(1999). When the economy has an infinity countable number of states, the paper establishes a financial equilibrium with a mild assumption in this incomplete market. In this case, the characteristic of equilibrium price whose norm is $1$, provides  an advantage of this approach. Latest version available upon request

3. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu Lemma, Brouwer and Kakutani fixed points theorems" with Pascal Gourdel,  Cuong Le Van and Ngoc Sang Pham (submitted) 

Abstract: This paper uses the Hartman-Stampacchia theorems as the primary tool to prove the GaleNikaidô-Debreu lemmas. It also establishes a full equivalence circle among the Hartman Stampacchia theorems, the Gale-Nikaidô-Debreu lemmas, and Kakutani and Brouwer fixedpoint theorems.  Latest version

4.   "Incomplete markets with a countable number of states: Equilibrium and No-Arbitrage " with Jean-Marc Bonnisseau and Cuong Le Van (forthcoming in Annals of Economics and Statictics)

Abstract: In this paper, we prove the existence of an equilibrium in a two-period model à la Hart with incomplete markets and a countable number of states. Moreover, under some restrictions on the returns matrix, an equilibrium asset price is a no-arbitrage price. Conversely, we consider a sequence of equilibria corresponding to an increasing number of states associated with a given no-arbitrage asset price. If the sequence of commodity prices has a non-zero cluster point for the product topology, then the limits of these prices and of the allocations (assets, commodities) constitute, together with the given asset price, an equilibrium with a countable number of states. Latest version available upon request

Work in Progress

5. Shocks of productivity in economies  

6.  Hartman-Stampacchia theorem and Gale-Nikaido-Debreu Lemma in infinite dimensional spaces