Learn More
We establish duality, existence and uniqueness results for a class of mass transportations problems. We extend a technique of W. Gangbo 9] using the Euler Equation of the dual problem. This is done by introducing the h-Fenchel Transform and using its basic properties. The cost functions we consider satisfy a generalization of the so-called Spence-Mirrlees(More)
Given a bounded open subset Ω of R d and two positive weight functions f and g, the Cheeger sets of Ω are the subdomains C of finite perimeter of Ω that maximize the ratio C f (x) dx ∂ * C g(x) dH d−1. Existence of Cheeger sets is a well-known fact. Uniqueness is a more delicate issue and is not true in general (although it holds when Ω is convex and f ≡ g(More)
We consider a class of law invariant utilities which contains the Rank Dependent Expected Utility (RDU) and the cumulative prospect theory (CPT). We show that the computation of demand for a contingent claim when utilities are within that class, although not as simple as in the Expected Utility (EU) case, is still tractable. Specific attention is given to(More)
  • G Carlier, I Ekeland, Robert E Lucas, Esteban Rossi
  • 2003
Following the recent analysis of Lucas and Rossi-Hansberg [10], we study the equilibrium structure of cities. By adopting a different (monetary) specification of commuting costs, we are able to prove the existence of equilibrium in more general situations: non-circular cities, or multi-sectorial production. The main mathematical tool in this paper is the(More)
This paper characterizes the core of a differentiable convex distortion of a probability measure on a non atomic space by identifying it with the set of densities which dominate the derivative of the distortion, for second order stochastic dominance. Furthermore the densities that have the same distribution as the derivative of the distortion are the(More)
In vivo oxidative capacity varies with muscle and training status in young adults energetics Antioxidants and aging: NMR-based evidence of improved skeletal muscle perfusion and Lower energy cost of skeletal muscle contractions in older humans skeletal muscle mitochondria play a role? Impairment of maximal aerobic power with moderate hypoxia in endurance(More)
This paper is motivated by a large variety of convex or non convex problems arising in symmetric and asymmetric information models. An existence theorem is proven, based on a supermodular version of Hardy-Littlewood's rearrangement inequalities. Sufficient conditions for monotonicity of optimal solutions are provided. Several applications to insurance are(More)