Publications des chercheurs de PSE

We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a financial structure with possibly long-term assets. We address the question of the continuity of the set of marketable payoffs with respect to the asset prices. In a previous paper, we have exhibited a sufficient condition,which is based only on the returns of the assets.However, it is never satisfied in the structures with re-trading [See Bonnisseau and Chéry (Ann Finance 10:523–552, 2014)], which is a very common feature in many papers following the model of Magill and Quinzii (Theory of Incomplete Markets, MIT Press, Cambridge, 1996). The main purpose of this paper is to address this issue. We exhibit a new sufficient condition for general financial structures, which enjoys the property to be inherited by the re-trading extension of a financial structure. So, we pave the way for equilibrium existence results under assumptions only on the fundamentals of the economy.

We study the existence of quasi-equilibria and equilibria for pure exchange economies with consumption externalities and Arrowian markets with personalized Lindahl prices. We provide examples showing first that quasi-equilibria and equilibria of the externality economy fail to exist under assumptions guaranteeing existence for economies without externalities. We show that the externality economy has identical equilibrium allocations of an appropriately defined constant returns to scale production economy without externalities. We exploit this equivalence to map sufficient conditions for the existence of quasi-equilibria and equilibria of the production economy into sufficient conditions of the pure exchange economy with externalities, thereby unveiling suitable irreducibility conditions and survival conditions.

The purpose of this paper is to prove the existence of a marginal pricing economic equilibrium in presence of increasing returns and externalities in a commodity space general enough as to encompass the vast majority of economic situations. This extends the existing literature on competitive equilibria in vector lattices by incorporating market failures, and it also generalises several non-competitive existence results to a larger class of commodity spaces. The key features are a suitable definition for the marginal pricing rule and an adaptation of the properness condition.

In this paper, we consider an economy with infinitely many commodities and market failures such as increasing returns to scale and external effects or other regarding preferences. The commodity space is a Banach lattice possibly without interior points in the positive cone in order to include most of the relevant commodity spaces in economics. We propose a new definition of the marginal pricing rule through a new tangent cone to the production set at a point of its (non-smooth) boundary. The major contribution is the unification of many previous works with convex or non-convex production sets, smooth or non-smooth, for the competitive equilibria and for the marginal pricing equilibria, with or without external effects, in finite-dimensional spaces as well as in infinite-dimensional spaces. In order to prove the existence of a marginal pricing equilibria, we also provide a suitable properness condition on non-convex technologies to deal with the emptiness of the interior of the positive cone.

In this paper, we consider a production economy with an unbounded attainable set where the consumers may have non-complete non-transitive preferences. To get the existence of an equilibrium, we provide an asymptotic property on preferences for the attainable consumptions and we use a combination of the nonlinear optimization and fixed point theorems on truncated economies together with an asymptotic argument. We show that this condition holds true if the set of attainable allocations is compact or, when the preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of [N. Allouch, An equilibrium existence result with short selling, J. Math. Econom. 37 2002, 2, 81–94] and covers the example of [F. H. Page, Jr., M. H. Wooders and P. K. Monteiro, Inconsequential arbitrage, J. Math. Econom. 34 2000, 4, 439–469] when the attainable utility levels set is not compact. So we extend the previous existence results with non-compact attainable sets in two ways by adding a production sector and considering general preferences.

We prove that under mild conditions individually rational Pareto optima will exist even in the presence of non-convex preferences. We consider decision-makers (DMs) dealing with a countable flow of pay-offs or choosing among financial assets whose outcomes depend on the realization of a countable set of states of the world. Our conditions for the existence of Pareto optima can be interpreted as a requirement of impatience in the first context and of some pessimism or not unrealistic optimism in the second context. A non-existence example is provided when, in the second context, some DM is too optimistic. We furthermore show that at an individually rational Pareto optimum at most one strictly optimistic DM will avoid ruin at each state or date. Considering a risky context, this entails that even if risk averters will share risk in a comonotonic way as usual, at most one classical strong risk lover will avoid ruin at each state or date. Finally, some examples illustrate circumstances when a risk averter could take advantage of sharing risk with a risk lover rather than with a risk averter.

In a stochastic financial exchange economy, two financial structures are equivalent if, for each given state price, the marketable payoffs are identical for the associated asset prices. The key property of two equivalent financial structures is that, when associated with any standard exchange economy, they lead to the same financial equilibrium. We exhibit a sufficient condition for the equivalence of two financial structures without re-trading with possibly long-term assets. We then apply this result to financial structures built upon primitive assets and their re-trading. We also borrow an assumption from Bonnisseau and Chéry (Ann Financ 10:523–552, 2014) to prove the equivalence between a financial structure and its reduced forms.

We investigate the problem of optimal investment and consumption of Merton in the case of discrete markets in an infinite horizon. We suppose that there is frictions in the markets due to loss in trading. These frictions are modeled through nonlinear penalty functions and the classical transaction cost and liquidity models are included in this formulation. In this context, the solvency region is defined taking into account this penalty function and every investigator have to maximize his utility, that is derived from consumption, in this region. We give the dynamic programming of the model and we prove the existence and uniqueness of the value function.

We consider a family of exchange economies with complete markets where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number, local differentiable selections of the equilibrium prices. Thus, even if ambiguity aversion is represented by non-differentiable multiprior preferences, economies retain generically the properties of the differentiable approach.

We consider a pure exchange overlapping generations economy with a varying number of commodities and consumers per period having possibly non-complete non transitive preferences. We provide a geometric and direct proof of the Balasko-Shell characterization of Pareto optimal allocations. As a by-product, we compute an explicit Pareto improving transfer when the criterion is not satisfied, which is minimal for some suitable distance.

Penser et préparer ce e transi on de- mande d’adopter une perspective transversale sur l’évolution des sociétés. L’université Paris 1 Panthéon-Sorbonne est l’un des principaux centres d’élabora on de la pensée contemporaine en sciences humaines et sociales en Europe et donc le lieu idéal pour catalyser l’émergence de ces nouveaux savoirs. Les textes présentés dans la première par e de cet ouvrage, issus de contributions à la conférence « Dynamiques sociales et changement climatique » qui s’est déroulée du 27 au 30 octobre 2015 à Paris 1, donnent un aperçu des rapports que l’université o re à l’analyse des enjeux socio-économiques du changement climatique.

We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a financial structure with possibly long-term assets. We exhibit a sufficient condition under which the set of marketable payoffs depends continuously on the arbitrage free asset prices. This generalizes previous results of Angeloni-Cornet and Magill-Quinzii involving only short-term assets. We also show that, under the same condition, the useless portfolios do not depend on the arbitrage free asset prices. We then provide an existence result of financial equilibrium for long term nominal assets for any given state prices with assumptions only on the fundamental datas of the economy.