Showing papers by "Paris Dauphine University published in 2002"

An introduction to the economy of the knowledge society

Abstract: This introductory article reviews the main themes relating to the development of new knowledge-based economies. After placing their emergence in historical perspective and proposing a theoretical framework which distinguishes knowledge from information, the authors characterize the specific nature of such economies. They go on to deal with some of the major issues concerning the new skills and abilities required for integration into the knowledge-based economy; the new geography that is taking shape (where physical distance ceases to be such an influential constraint); the conditions governing access to both information and knowledge, not least for developing countries; the uneven development of scientific, technological (including organizational) knowledge across different sectors of activity; problems concerning intellectual property rights and the privatization of knowledge; and the issues of trust, memory and the fragmentation of knowledge.

Impulse differential inclusions: a viability approach to hybrid systems

Abstract: Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples.

Asymptotics and calibration of local volatility models

Abstract: We derive a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation. Using this equation we establish closed-form asymptotic formulae for the implied volatility near expiry as well as for deep in- and out-of-the-money options. This in turn leads us to propose a new formulation near expiry of the calibration problem for the local volatility model, which we show to be well posed.

Selected new aspects of the calculus of variations in the large

Abstract: We discuss some of the recent developments in variational methods while emphasizing new applications to nonlinear problems We touch on several issues: (i) the formulation of variational set-ups which provide more information on the location of critical points and therefore on the qualitative properties of the solutions of corresponding Euler-Lagrange equations; (ii) the relationships between the energy of variationally generated solutions, their Morse indices, and the Hausdorff measure of their nodal sets; (iii) the gluing of several topological obstructions; (iv) the preservation of critical levels after deformation of functionals; (v) and the various ways to recover compactness in certain borderline variational problems

Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities

Abstract: When estimating hydraulic transmissivity the question of parametrization is of great importance. The transmissivity is assumed to be a piecewise constant space-dependent function and the unknowns are both the transmissivity values and the zonation, the partition of the domain whose parts correspond to the zones where the transmissivity is constant. Refinement and coarsening indicators, which are easy to compute from the gradient of the least squares misfit function, are introduced to construct iteratively the zonation and to prevent overparametrization.

Pure jump Lévy processes for asset price modelling

Abstract: The goal of the paper is to show that some types of Levy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Levy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these processes are related to Brownian motion, the central process in finance, through stochastic time changes which can in turn be interpreted as a measure of the economic activity. Lastly, we focus on two particular classes of pure jump Levy processes, the generalized hyperbolic model and the CGMY models, and report on the goodness of fit obtained both on stock prices and option prices.

Ownership Structure and Open Market Stock Repurchases in France

Abstract: This paper examines open market stock repurchases in France We find an average positive market reaction on the announcement However, the magnitude of price reaction is found to be dependent on a number of measures of corporate governance structure The positive aspects of the announcement surface only for a company with a low likelihood of takeover and a low risk of minority shareholder expropriation Specifically, stock repurchase programs are good news when the firm is supported by foreign institutional investors, and in the case of controlled firms, when the firm has a second major shareholder, which guarantees an effective balance of power to the controlling shareholders

Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

Abstract: A steady state fluid-structure interaction problem is considered and its solvability is studied. Both the fluid and the structure are three-dimensional. The equations of the viscous fluid motion are set in an unknown domain depending on the structure displacement. The structure is elastic and its deformation depends on the stress coming from the fluid. We prove that, for small enough applied exterior forces, there exists at least one regular solution of this nonlinear coupled problem.

CHAPTER 14 – Set-Valued Integration and Set-Valued Probability Theory: An Overview

Abstract: This chapter presents an overview of set-valued integration and set-valued probability theory. The mathematical modelization based on multifunctions has shown its great adaptability and relevance for a long time. The integration of strongly measurable multifunctions with those that can be approximated by simple measurable multifunctions in the sense of the Hausdorff distance is analyzed in the chapter. The weakly measurable multifunctions in connection with graph-measurability are presented in the chapter. The Hiai–Umegaki set-valued conditional expectation is examined and set-valued measures are considered in the chapter. The definition and the main properties of set-valued martingales and some basic facts about Gaussian multifunctions and the set-valued central limit theorem are presented in the chapter. The integration of strongly measurable multifunctions is elaborated in the chapter. It allows for a lot of stability properties and for general results of existence of measurable selections, especially in connection with the graph measurability. It is shown in the chapter that the measurability of a closed-valued multifunction can be expressed in terms of distance functions and is connected with the notion of Castaing representation.

On some periodic Hartree-type models for crystals

Abstract: Nous poursuivons dans cet article notre etude systematique de la limite thermodynamique de divers modeles issus de la Chimie Quantique Moleculaire. Nous etudions plus specifiquement les modeles de Hartree et de Hartree restreint. Pour le modele de Hartree restreint, nous prouvons l'existence de la limite thermodynamique de l'energie par unite de volume. Nous definissons egalement un modele periodique associe au modele de Hartree, et nous demontrons qu'il est bien pose.

The epidemiology, economics and quality of life burden of age-related macular degeneration in France, Germany, Italy and the United Kingdom.

Abstract: Age-related macular degeneration (AMD) is a major public health issue, but little is known about the economics of the disease. This contribution describes the epidemiology and the economics of AMD in four European countries: France, Germany, Italy and the United Kingdom (UK). We reviewed published information on AMD, including guidelines, official statistics, and local literature and interviewed AMD experts. All available health-related quality of life studies (HRQoL) on AMD were also reviewed. Data collection focused on epidemiology, medical management and resource use (both medical and non-medical items). Prevalence of AMD among persons older than 65 years is 8% and increases with age. There are two forms of the disease: atrophic (80–85% of AMD cases) and exudative, which is characterised by choroidal neovascularisation (CNV; 15–20% of AMD cases). No treatment for the atrophic form is available. Laser photocoagulation is the mainstay of treatment for CNV, although less than 30% of persons with CNV can benefit from it. Photodynamic therapy (PDT), a new treatment for CNV, reduces the risk of vision loss in forms with predominantly visible lesions. Several other new procedures are also under development. Rehabilitation and low-vision aids are useful palliative interventions when there is a residual visual acuity. The yearly budget impact of AMD was found to be between 51.3 and 101.1 million euros in the four countries studied. Information on social services and resource use was scant and little is reported on the impact of AMD on HRQoL. Economic studies of AMD should be conducted in order to assist public health decision making.

Convergence to equilibrium for semilinear parabolic problems in

Abstract: We consider the semilinear parabolic equation on , assuming that f is an arbitrary C 1 function satisfying and . We prove that any bounded positive solution that decays to zero at spatial infinity, uniformly with respect to t, converges to a (single) stationary solution as . Our proof combines energy and comparison techniques with dynamical system arguments. We first establish an asymptotic symmetrization result: as , approaches a set of steady states that are radially symmetric about a common origin in . To this aim we introduce a new tool that we call first moments of energy. Having established the symmetrization, we apply a general convergence result for gradient-like dynamical systems. This amounts to showing that the dimension of the kernel of the linearized operator around an equilibrium w matches the dimension of a manifold of equilibria passing through w.

From Concordance / Discordance to the Modelling of Positive and Negative Reasons in Decision Aiding

Abstract: The principle of concordance/discordance was introduced by B. Roy in his very early work on Multiple Criteria Decision Analysis. Although such a principle is grounded by strong evidence from real life decision situations, the way in which it has been implemented in existing MCDA methods allows only for its partial and limited use. Indeed, the principle lacks a theoretical frame enabling a more general use in decision analysis. The paper presents a possible generalisation of this principle under the concepts of positive and negative reasons. For this purpose, a new formalism, (a four valued logic) is suggested. Under such a formalism the concordance test is seen as the evaluation of the existence of positive reasons supporting the sentence “x is at least as good as y”, while the discordance test can be viewed as the evaluation of the existence of negative reasons against the same sentence. A number of results obtained in preference modelling and aggregation shows the potentiality of this approach.

Weighted Node Coloring: When Stable Sets Are Expensive

Abstract: A version of weighted coloring of a graph is introduced: each node v of a graph G = (V, E) is provided with a positive integer weight w(v) and the weight of a stable set S of G is w(S) = max{w(v) : v ? V ? S} A k-coloring S = (S1, , Sk) of G is a partition of V into k stable sets S1, , Sk and the weight of S is w(S1) + + w(Sk) The objective then is to find a coloring S = (S1, , Sk) of G such that w(S1) + + w(Sk) is minimized Weighted node coloring is NP-hard for general graphs (as generalization of the node coloring problem) We prove here that the associated decision problems are NP-complete for bipartite graphs, for line-graphs of bipartite graphs and for split graphs We present approximation results for general graphs For the other families of graphs dealt, properties of optimal solutions are discussed and complexity and approximability results are presented

Smooth Solutions of systems of quasilinear parabolic equations

Abstract: We consider in this article diagonal parabolic systems arising in the context of stochastic dierential games. We address the issue of nding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic dierential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be the adequate one to achieve the regularity property. A key step in the theory is to prove the existence of Holder solution. Mathematics Subject Classication. 35XX, 49XX.

A first-order, four valued, weakly paraconsistent logic and its relation to rough sets semantics

Abstract: A first order four-valued logic, called DDT, is presented in the paper as an extension of Belnap’s logic using a weak negation and establishing an appropriate semantic for the predicate calculus. The logic uses a simple algebraic structure, that is the smallest non trivial interlaced bilattice on the four truth values, thus resulting in a boolean algebra on the set of truth values. The logic is a language for reasoning under uncertainty, enabling to capture hesitation due either to inconsistent or incomplete information, while keeping a clear distinction between these epistemic states. The logic was originally developed for preference modelling purposes (for which a brief account is given in the paper). The paper demonstrates and discusses the equivalence between the semantics of this logic and of rough sets semantics. On this basis, this papers presents the possibility of inducing rules from examples, that can be integrated in systems whose inference is expressed in the above logic. Such an approach enhances the potentialities of the use of rough sets in classification, reasoning and decision support.

Belief extrapolation (or how to reason about observations and unpredicted change)

Abstract: We give a logical framework for reasoning with observations at different time points. We call belief extrapolation the process of completing initial belief sets stemming from observations by assuming minimal change. We give a general semantics and we propose several extrapolation operators. We study some key properties verified by these operators and we address computational issues. We study in detail the position of belief extrapolation with respect to revision and update: in particular, belief extrapolation is shown to be a specific form of time-stamped belief revision. Several related lines of work are positioned with respect to belief extrapolation.

On Equilibria when Agents Have Multiple Priors

Abstract: We discuss the existence and the qualitative properties of equilibria when agents have multiple priors and there is only one good in each state of the world. We first prove a general existence result in infinite dimension economies. We then fully describe the equilibria in two special cases. We first consider the case of CEU maximizers that have same capacities. We next consider the case of no aggregate uncertainty. We prove that if agents have non-random initial endowments and are uncertainty averse and maximize the minimal expected utility according to a set of possible priors, then the existence of a common prior is equivalent to the existence of a unique equilibrium, the no-trade equilibrium. We lastly give a mild assumption for indeterminacy of equilibria and compute the dimension of indeterminacy.

Grouping Connected Components using Minimal Path Techniques

Abstract: We address the problem of finding a set of contour curves in a 2D or 3D image. We consider the problem of perceptual grouping and contour completion, where the data is an unstructured set of regions in the image. A new method to find complete curves from a set of edge points is presented. Contours are found as minimal paths between connected components, using the fast marching algorithm. We find the minimal paths between each of these components, until the complete set of these “regions” is connected. The paths are obtained using backpropagation from the saddle points to both components.