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227
2002): “Envelope Theorems for Arbitrary Choice Sets
 Econometrica
"... The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the tradi ..."
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Cited by 185 (8 self)
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The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left and rightdifferentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddlepoint problems, problems with parameterized constraints, and optimal stopping problems.
Topographic Maps and Local Contrast Changes in Natural Images
 Int. J. Comp. Vision
, 1999
"... . We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of ..."
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Cited by 80 (9 self)
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. We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusiontransparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. Keywords: topographic map, mathematical morphology, level set, junctions, contrast changes, digitization 1.
Networks in Labor Markets: Wage and Employment Dynamics and Inequality
 CALVÓARMENGOL, ANTONI AND YANNIS IOANNIDES (2005) “SOCIAL NETWORKS IN LABOR MARKETS,” IN THE NEW PALGRAVE, L. BLUME AND S. DURLAUF (EDS), LONDON: MACMILLAN PRESS (IN PRESS) GRANOVETTER, MARK
, 2003
"... We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and exp ..."
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Cited by 56 (4 self)
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We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wages, in the sense of first order stochastic dominance. A similar effect results from an increase in the network contacts of an agent. In terms of dynamics and patterns, we show that both wages and employment are positively associated (a strong form of correlation) across time and agents. We also analyze the decisions of agents regarding staying in the labor market or dropping out. If there are costs to staying in the labor market, and we compare two networks of agents that are identical except that one group starts with a worse wage status, then that group's dropout rate will be higher than the other's and there will be a persistent di#erence in wages between the groups.
Expected Utility Theory without the Completeness Axiom,”Journal of Economic Theory, Volume 115, Issue 1
, 2004
"... We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a mul ..."
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Cited by 38 (6 self)
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We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multiutility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a welldefined sense.
Comparative Statics by Adaptive Dynamics and The Correspondence Principle
 Econometrica
, 2000
"... This paper formalizes the relation between comparative statics and the outofequilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o# learning dynamics that involve larger values of the endoge ..."
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Cited by 35 (7 self)
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This paper formalizes the relation between comparative statics and the outofequilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o# learning dynamics that involve larger values of the endogenous variables. Second, equilibrium selections that are not monotone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent. JEL Classification: C61, C62, C72, C73 Keywords: Monotone comparative statics, supermodularity, strategic complements, learning, correspondence principle. # Discussions with Ilya Segal and Chris Shannon were very important for this work, I am very grateful for all their help. For comments and advice, I also thank Robert Anderson, Juan Dubra, Nestor Gandelman, Ernesto Lopez Cordova, Marcelo Moreira, Charles Pugh, Matthew Rabin, Tarun Sabarwal and Miguel Villa...
Optimal Unemployment Insurance, with Human Capital Depreciation, and Duration Dependence.
, 2003
"... This paper studies the effect of human capital depreciation and duration dependence on the design of an optimal unemployment insurance (UI) scheme. Our results partially confirm those obtained in most previous studies: benefits should decrease with unemployment duration. The optimal program also gen ..."
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Cited by 28 (5 self)
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This paper studies the effect of human capital depreciation and duration dependence on the design of an optimal unemployment insurance (UI) scheme. Our results partially confirm those obtained in most previous studies: benefits should decrease with unemployment duration. The optimal program also generates two main novel features, which are not present in stationary models. First, if human capital depreciates rapidly enough during unemployment, UI transfers are bounded below by a minimal “assistance” level that arises endogenously in the efficient program. Second, we study the optimality of imposing a history contingent wage tax after reemployment. Our numerical simulations based on the Spanish and US economies show that the wage tax should decrease with the length of worker’s previous unemployment spell, and become a wage subsidy for longterm unemployed workers. As a byproduct of our study, we develop a systematic approach suitable for studying recursively a wide range of dynamic moralhazard problems, and other models with similar characteristics.
Vectorvalued coherent risk measures
 Finance and Stochastics
, 2004
"... We define (d, n)−coherent risk measures as setvalued maps from L ∞ d into IRn satWe show that this definition is a convenient extension of the isfying some axioms. realvalued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passa ..."
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Cited by 27 (0 self)
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We define (d, n)−coherent risk measures as setvalued maps from L ∞ d into IRn satWe show that this definition is a convenient extension of the isfying some axioms. realvalued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from IR d−valued random portfolio to IR n−valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided. 1
On the extension of the NamiokaKlee theorem and on the Fatou property for risk measures
 in Optimality and Risk: Modern Trends in Mathematical Finance, The Kabanov Festschrift
, 2009
"... This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de
ned on spaces of random variables, possibly with the socalled Fatou property. We show
rst that the celebrated NamiokaKlee theorem for linear, positive functionals h ..."
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Cited by 27 (7 self)
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This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de
ned on spaces of random variables, possibly with the socalled Fatou property. We show
rst that the celebrated NamiokaKlee theorem for linear, positive functionals holds also for convex monotone maps on Frechet lattices. It is wellknown among the specialists that the Fatou property for risk measures on L1 enables a simpli
ed dual representation, via probability measures only. The Fatou property in a general framework of lattices is nothing but the lower order semicontinuity property for . Our second goal is thus to prove that a similar simpli
ed dual representation holds also for order lower semicontinuous, convex and monotone functionals de ned on more general spaces X (locally convex Frechet lattices). To this end, we identify a link between the topology and the order structure in X the Cproperty that enables the simpli
ed representation. One main application of these results leads to the study of convex risk measures de ned on Orlicz spaces and of their dual representation. Acknowledgements The
rst author would like to thank B. Rudlo¤, P. Cheridito and A. Hamel for some discussions while she was visiting the ORFE
A Model of Farsighted Voting
, 2008
"... I present a new method of interpreting voter preferences in settings where policy remains in effect until replaced by new legislation. In such settings voters consider not only the utility they receive from a given policy today, but also the utility they will receive from policies likely to replace ..."
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Cited by 26 (0 self)
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I present a new method of interpreting voter preferences in settings where policy remains in effect until replaced by new legislation. In such settings voters consider not only the utility they receive from a given policy today, but also the utility they will receive from policies likely to replace that policy in the future. The model can be used to both characterize longterm preferences and distributions over policy outcomes in situations where policy is ongoing and voters are farsighted.