Showing papers by "Paris Dauphine University published in 1997"
TL;DR: In this paper, the authors extend the results of Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated.
Abstract: In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their “admissible arbitrage prices.”
247 citations
TL;DR: In this paper, the authors established the convexity of a viscosity solution of a general second-order fully nonlinear elliptic equation with state constraints boundary conditions, and they combined a comparison principle with the observation that, under suitable assumptions, the convolutional envelope of the solution is a supersolution.
195 citations
TL;DR: In this paper, the authors show that weak solutions of Navier-Stokes equations in T2 turn out to be smooth as long as the density remains bounded in L∞(T2).
Abstract: Regularity of weak solutions of the compressible isentropic Navier-Stokes equations is proven for small time in dimension N = 2 or 3 under periodic boundary conditions. In this paper, the initial density is not required to have a positive lower bound and the pressure law is assumed to satisfy a condition that reduces to τ > 1 when N = 2 and p(φ) = aφτ. Moreover,weak solutions in T2turn out to be smooth as long as the density remains bounded in L∞( T2).
151 citations
TL;DR: An adaptative coupling of the Boltzmann and Navier?Stokes equations to compute hypersonic flows around a vehicle at high altitude is introduced here for monoatomic gases.
127 citations
TL;DR: In this article, the authors address the issue of path-dependent selection and inefficiency, counterfactual methods and empirical evidence employed in this research trajectory, and ask whether these results suggest a large welfare loss.
125 citations
TL;DR: In this article, the Navier-Stokes equations for two-dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity without assuming positive lower bounds on the initial density.
Abstract: Global regularity results for weak solutions of the Navier-Stokes equations for two-dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity without assuming positive lower bounds on the initial density. As an application, we deduce regularity properties for the integral curves of the corresponding velocity field. Finally, we prove regularity results “in the small” for strong solutions.
124 citations
Journal Article•
01 Dec 1997-Dynamics of Continuous Discrete and Impulsive Systems-series B-applications & Algorithms
121 citations
TL;DR: This work surveys approximation algorithms for some well-known and very natural combinatorial optimization problems, and discusses how one can relate the approximability behavior (from both a positive and a negative point of view) of vertex covering to the approximation behavior of a restricted class of independent set problems.
Abstract: We survey approximation algorithms for some well-known and very natural combinatorial optimization problems, the minimum set covering, the minimum vertex covering, the maximum set packing, and maximum independent set problems; we discuss their approximation performance and their complexity. For already known results, any time we have conceived simpler proofs than those already published, we give these proofs, and, for the rest, we cite the simpler published ones. Finally, we discuss how one can relate the approximability behavior (from both a positive and a negative point of view) of vertex covering to the approximability behavior of a restricted class of independent set problems.
117 citations
TL;DR: New results using viability theory are provided that allow us to study optimal time functions free from the controllability assumptions classically made in the partial differential equations approach.
Abstract: We study optimal times to reach a given closed target for controlled systems with a state constraint. Our goal is to characterize these optimal time functions in such a way that it is possible to compute them numerically and we do not need to compute trajectories of the controlled system. In this paper we provide new results using viability theory. This allows us to study optimal time functions free from the controllability assumptions classically made in the partial differential equations approach.
113 citations
01 Jun 1997
TL;DR: IusWare (IUStitia SoftWARis) is a methodology designed to evaluate software products in a formal and rigorous way based on the multicriteria decision aid approach.
Abstract: IusWare (IUStitia SoftWARis) is a methodology designed to evaluate software products in a formal and rigorous way. The methodology is based on the multicriteria decision aid approach and encompasses activities such as the comparison, assessment and selection of software artefacts. The methodology defines an evaluation process which consists of two main phases: designing an evaluation model and applying it. The design phase is made up of the following activities: (1) identifying the actors that are relevant to the evaluation, their roles, the purpose of the evaluation, the resources available and the object(s) of the evaluation; (2) identifying the type of evaluation required: either a formal description of products or the ranking of products from the most preferred to the least preferred, or a partitioning into two sets of the best and the remaining products; (3) defining a nonredundant hierarchy of evaluation attributes, often corresponding with the quality characteristics of quality models; (4) associating a measure, a criterion scale and a function to transform the measure scale into the criterion scale to each basic attribute; and (5) choosing an aggregation technique so as to aggregate values on criteria to form a recommendation for the selection. In the application phase, attributes of products are measured, the measures are transformed into values on criteria and aggregated to form a recommendation.
103 citations
TL;DR: A reduced reachability graph called symbolic reachabilitygraph is presented that can be constructed directly by an efficient algorithm without considering the actual state space of the model and its analysis provides equivalent results as the analysis of the ordinary reachable graph.
TL;DR: In this paper, the authors conjecture that organizational actors, through their actions, create their own context, and that the context tends to develop a dynamic of its own, which escapes the control of the organizational actors.
Abstract: In this article we conjecture that organizational actors, through their actions, create their own context. Once initiated, the context tends to develop a dynamic of its own, which escapes the control of the organizational actors. In con sequence, the context becomes the determining factor of the actors' initiatives. Voluntarism has created its own determinism which will eventually shape the organizational actors' futures. To illustrate our view, we study a crisis which we believe may exemplify a situation induced and perpetuated by the same organizational actors who tried to handle it. To support this thesis, we attempt to show that the observed crisis is chaotic. Our results reveal that deterministic chaos cannot be rejected as an explanation of the dynamics of the situation. The crisis exhibits an apparently random behaviour which, we believe, is deter ministically created through tightly coupled actions and dynamic interactions among actors. Once in the chaotic state, actors cannot control the process ...
TL;DR: In this article, the existence, multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation were investigated, and it was shown that there exists an infinite number of connected branches of solutions which bifurocate from the bottom of the essential spectrum of the corresponding linear operator.
TL;DR: In this article, the authors introduce and study the minimal time of a crisis map, which measures the minimum time spent outside a given closed domain of constraints by trajectory solutions of a differential inclusion.
Abstract: In this paper, we introduce and study the minimal time of a crisis map which measures the minimal time spent outside a given closed domain of constraints by trajectory solutions of a differential inclusion The interest of such a notion is basically to tackle simultaneously viability and target issues The main mathematical result characterizes the epigraph of the crisis map in terms of a viability kernel of an augmented problem This allows the obtaining of the numerical schemes we specify and to derive an equivalent Hamilton–Jacobi formulation A simple economic example illustrates the results
TL;DR: The existence of the ergodic attractor is shown in Theorems 1 and 2 in this paper, and the existence of qualitative properties exist behind the convergence of the terms λuλ(x), ≠ u(x,T) in the Hamilton-Jacobi-Bellman equations (HJBs) as λ tends to + 0, T goes to +∞, to the unique number.
Abstract: The problem of the convergence of the terms λuλ(x), ≠ u(x,T) in the Hamilton-Jacobi-Bellman equations (HJBs) as λ tends to +0, T goes to +∞, to the unique number is called the ergodic problem of the HJBs. We show in this paper what kind of qualitative properties exist behind this kind of convergence. The existence of the ergodic attractor is shown in Theorems 1 and 2. Our solutions of HJBs satisfy the equations in the viscosity solutions sense.
TL;DR: The purpose of this paper has been to trace the development of a way of thinking and type of research which first saw the light of day in France, but which for many years have been influenced and supplemented by work carried out in other European countries.
TL;DR: In this paper, the existence of strong and variational-weak solutions for the multivalued stochastic differential equation was proved for strong solutions and remains open for variational weak solutions.
Abstract: In this paper one studies the existence of strong and variational-weak solutions for the multivalued stochastic differential equation The uniqueness is proved for strong solutions and remains open for variational-weak solutions
TL;DR: In this article, the boundary of the victory domain is shown to be a nonsmooth semipermeable surface, i.e., a solution of the Isaacs equation.
Abstract: We study the target problem which is a differential game where one of the players aims at reaching a target while the other player aims at avoiding this target forever We characterize the victory domains of the players by means of geometric conditions and prove that the boundary of the victory domains is a nonsmooth semipermeable surface, ie, is a solution (in a weak sense) of the Isaacs equation: supuinfv 〈f (x, u, v),p〉 = 0, wheref is the dynamic of the system,u andv are the respective controls of the players, andp is a normal to the boundary of the victory domains at the pointx
TL;DR: The bacteriocins lactococcin B and pediocin PA-1 were purified by ethanol precipitation, preparative isoelectric focusing, and ultrafiltration reproducibly leads to high final yields in comparison to the generally low yields obtained by column chromatography.
Abstract: The bacteriocins lactococcin B and pediocin PA-1 were purified by ethanol precipitation, preparative isoelectric focusing, and ultrafiltration. The procedure reproducibly leads to high final yields in comparison to the generally low yields obtained by column chromatography. Specifically, during isoelectric focusing no loss of activity occurs. The method, in general, should be applicable to small, hydrophobic, cationic bacteriocins.
01 Jan 1997
TL;DR: Personal reflections on the evolution of interactive multiple criteria procedures trace their development from early roots in mathematical programming and suggest some directions for future developments.
Abstract: This paper offers personal reflections on the evolution of interactive multiple criteria procedures. We trace their development from early roots in mathematical programming. During this early period, the theoretical and technical challenges of computing candidate solutions dominated the research. Later, major challenges arose from consideration of the behavioral aspects of decision processes. We further discuss what we consider to be current challenges and suggest some directions for future developments.
TL;DR: The results established the long term impact of perennial rhinitis on quality of life (generic and specific), and raised questions about appropriate therapy, since a positive association between current use of non-anticholinergic antihistamines with improvements on some SF-36 dimensional scores in patients with perennial Rhinitis was observed.
Abstract: Our primary objective in designing the first large-scale nationwide population-based survey in France was to assess the impact of perennial rhinitis on quality of life Our secondary objective was to describe the use of drug treatment, including histamine H1 antagonists, in that population
01 Mar 1997
TL;DR: In this paper, le processus de creation and validation d'une echelle de mesure de la tendance a innover des consommateurs (l'ETIG), composee de trois dimensions: l'attrait pour la nouveaute, l'autonomie dans la decision d'innover and l'aptitude a prendre des risques en essayant la newavaute.
Abstract: Cet article presente le processus de creation et de validation d'une echelle de mesure de la tendance a innover des consommateurs (l'ETIG), composee de trois dimensions: l'attrait pour la nouveaute, l'autonomie dans la decision d'innover et l'aptitude a prendre des risques en essayant la nouveaute. L'hypothese sous-jacente est que la tendance a innover est un trait de personnalite central de l'individu, qui ne peut etre mesure que par l'ensemble de ses manifestations, en raison de son caractere latent. Les resultats montrent une bonne validite de l'echelle.
TL;DR: In this paper, the authors considered a dynamical game where the phenotypes of the predator and of the prey can vary, and the question at stake is the survival of each of the species, instead of the maximization of a given pay-off by each player, as it is commonly discussed in games.
Abstract: Lotka–Volterra equations are considered a dynamical game, where the phenotypes of the predator and of the prey can vary. This differs from the usual procedure of specifying as a priori laws according to which strategies are supposed to change. The question at stake is the survival of each of the species, instead of the maximization of a given pay-off by each player, as it is commonly discussed in games. The predator needs the prey, while the prey can survive without the predator.
01 Jan 1997
TL;DR: A basic distinction between uncertainty reasons is advanced in the paper, that is between lack of information and contradictory information, and the PC preference structure is adopted in order to represent the different preference situations that may occur.
Abstract: Uncertainty and ambiguity are common situations in decision aid and therefore in preference modelling and aggregation. A basic distinction between uncertainty reasons is advanced in the paper, that is between lack of information and contradictory information. A semantical investigation of this approach is conducted and the PC preference structure is adopted in order to represent the different preference situations that may occur. This type of preference structure, besides offering an enhanced granularity in preference modelling, is strongly axiomatized, enabling a precise calculus. Some of its potentialities are discussed using a preference aggregation problem.
TL;DR: In this paper, the authors considered the case where the symbol of the symbol is a critical value of a symbol, and proved the existence of a full asymptotic expansion for φ in terms of φ and ln ℏ and computed the leading coefficient.
TL;DR: This result essentially improves, from both complexity and approximation quality points of view, the best-known approximation ratio for maximum independent set.
TL;DR: A general framework for building intelligent distributed strategic decision making systems which integrates advances in both distributed decision making and Distributed Artificial Intelligence is presented and a multi-blackboard system, ARISTOTE, is described which is aimed at helping corporate managers address the feasibility and coherence of a plan of actions.
Abstract: The decision-making process in strategic planning is often too complex to be handled by conventional methods. Strategic planning problems (building new plans, new product planning, etc.) belong to the class of problems called ill-structured by H. Simon. They involve a decomposition of the main problem into a set of subproblems, a reasoning process at the subproblem level, and then a coordinated and aggregated process to build a global solution. Because partial solutions are generated without having a complete view of the global objective, this type of decision-making process very often generates incoherent and contradictory hypotheses and actions. Therefore, the main problem is to find a way to achieve coherence and coordination among decisions made locally by different agents, at different levels.
01 Jan 1997
TL;DR: In this article, a review of four lectures whose aim was to present some results on semi-classical methods for the Schrodinger equation obtained by using coherent states is presented.
Abstract: These notes cover and extend a review of four lectures whose aim was to present some results on semi-classical methods for the Schrodinger equation obtained by using coherent states. The goal was not to be by any mean exhaustive but rather to focus on applications susceptible to be related to some new -both numerical and experimental-recent results in quantum mechanics, with emphasis on the situations where the underlying classical system is chaotic.
TL;DR: In this article, the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or setvalued initial conditions, was proved.
Abstract: We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations. As an application we construct the value function of the Mayer problem arising in control theory.
Posted Content•
TL;DR: In this paper, the problem of portfolio rebalance with the payment of taxes on benefits is studied and an optimal strategy can always be chosen such that the agent never sells out of his portfolio and buy new Financial assets simultaneously.
Abstract: Here, we study the case where the portfolio rebalancement involves the payment of taxes on benefits. Then, the purchasing time of the asset to be sold has to be recorded in order to compute the amount of tax to be paid. In addition to the no-short-selling constraint, our model assumes that sales are subject to the first-in-first-out priority rule on sales. A precise description of the model is given in Section 2. The agent problem turns out to be a nonclassical optimal control problem with endogeneous delay andwith complex nonnegativity constraint on consumption. Section 3 is devoted to the proof of the following economic appealing result. An optimal strategy can always be chosen such that the agent never sells out of his portfolio and buy new Financial assets simultaneously. Using this property, the nonnegativity constraint on consumption is simplified and reduced to a classical constraint on the controls and the state variables. Namely, the nonnegativity constraint on consumption can be expressed simply in terms of the investment and the disinvestment functions. In Section 4, we assume some additional smoothness conditions on the optimal strategy in order to derive the first-order conditions associated to the control problem of interest. The usual variational methods are adapted to handle the endogeneous delay function.