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- G. Buttazzo, G. Carlier, M. Comte
- 2007

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)

- G. Carlier
- 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)

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the… (More)

- G. Carlier, R.-A. Dana
- 2004

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)

- G. Carlier
- 2011

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)

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials, deprivation and satisfaction quasi-orderings for the Lorenz… (More)

We consider a problem of derivatives design under asymmetry of information: the principal sells a contingent claim to an agent, the type of whom he does not know. More precisely, the principal designs a contingent claim and prices it for each possible agent type, in such a way that each agent picks the contingent claim and pays the price that the principal… (More)

- G. Carlier
- 2006

We consider a class of concave law invariant utilities which contains the Rank Dependent Expected Utility (RDU). For this class, we show that computation of the demand for a contingent claim, although not as simple as in the Expected Utility (EU) case, is still tractable. Specific attention is given to the RDU case. Numerous examples are fully solved.

- G. Carlier
- 2003

This paper studies optimal menus of debt contracts such as secured debentures or bonds, in the presence of diversity of opinions between borrowers and lenders. We first characterize incentive compatible contracts , then prove the existence of optimal debt contracts. Finally, we are able to explicitly characterize such optimal menus within a specific case:… (More)