Showing papers by "Paris Dauphine University published in 2000"

Order Flow, Transaction Clock, and Normality of Asset Returns

Abstract: The goal of this paper is to show that normality of asset returns can be recovered through a stochastic time change. Clark (1973) addressed this issue by representing the price process as a subordinated process with volume as the lognormally distributed subordinator. We extend Clark's results and find the following: (i) stochastic time changes are mathematically much less constraining than subordinators; (ii) the cumulative number of trades is a better stochastic clock than the volume for generating virtually perfect normality in returns; (iii) this clock can be modeled nonparametrically, allowing both the time-change and price processes to take the form of jump diffusions. The relations among trading volume, stock prices, and price volatility, the subject of empirical and theoretical studies over many years, have lately received renewed attention with the increased availability of high frequency data. A vast amount of research has focused on issues such as news arrivals, volume, and price changes or volatility moves, usually outside any framework of general or even partial equilibrium. Is the normality of returns-a key issue, for example, in the mean-variance paradigm for portfolio choice, or the recent study of the problems of risk management (e.g., in Value at Risk)-verified at any time horizon? The evidence accumulated from a number of studies that document the presence of leptokurtosis and skewness in the distribution of returns of a wide variety of financial assets suggests that the answer is no. Studies as early as, for example, Fama (1965), showed that daily returns are more long tailed than the normal density, with the distribution of returns approaching normality as the holding period is extended to one month. In the same manner, volatility smiles and other observed

Global solutions for some oldroyd models of non-newtonian flows

Abstract: The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.

Multicriterion analysis for sustainable water resources planning: a case study in spain

Abstract: The present article demonstrates the implementation of Multicriterion Decision Making (MCDM) analysis for a case study of Flumen Monegros irrigation area in the Huesca province of Spain. The criteria used to rank alternativesconsist of (1) economic factors including initial cost ofirrigation system, maintenance cost, profitability of crops,extent of European subsidies; (2) environmental factors whichcomprise water volume, water quality after irrigation, efficiency of the use of water, resistance to floods or droughts; (3) Social factors including employment of rurallabour, area non-cultivated. Alternative policies areformulated by mixing factors such as irrigation system, waterpricing, water allocation, crop distribution, fertiliser use,subsidies received. Multicriterion Sorting Technique (MCST)ELECTRE-TRI is employed to reduce the large size payoff matrixto predefined categories for further usage of MCDM techniques.Five MCDM techniques, namely, PROMETHEE-2, EXPROM-2, ELECTRE-3, ELECTRE-4, and Compromise Programming (CP) are employed torank the alternatives. Spearman rank correlation coefficientis employed to assess the correlation coefficient between theranking patterns obtained by the above MCDM techniques.Additive ranking principle is used for group decision makinganalysis. Results indicate that five MCDM techniques choosethe same alternative strategy as the preferred one.

Existence for an Unsteady Fluid-Structure Interaction Problem

Abstract: We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two fixed point procedures.

Fully nonlinear stochastic PDE with semilinear stochastic dependence

Abstract: We study in this Note scalar fully nonlinear stochastic second order partial differential equations, possibly, degenerate with a semilinear stochastic dependence We introduce a notion of stochastic viscosity solutions adapted to that class of equations And we show general existence, uniqueness and regularity results

Storage and Viability of a Fishery with Resource and Market Dephased Seasonalities

Abstract: In this study we analyse the role of the storageregulation in a fishery's production process when theresource exploited and the market to which theproduction is exported are characterized by seasonaldephased oscillations. For this purpose we built up adynamic model drawn from the French Guyana shrimpfishery example. The underlying objective of the modelis not the maximisation of a given criterion (as wouldbe in the optimal control approach), but merely themaintenance of the fishery's economical viability. Thefundamental principle is here to try to preserve asmany as possible viable control options. Theconditions to achieve and maintain this viability arecaptured in a certain number of constraints. Theanalysis points out periods and situations within theseason where the fishermen must anticipate theevolution of their storage to avoid violating thoseviability constraints. The study also indicates howthe fishery's viability can be ensured even if theexploitation costs exceed the commercial value of thelandings for a finite part of the year. However, whenthe resource's and/or market's oscillations are toolarge, the fishery may be not viable any longer and itappears that the crisis can not be removed byinvesting in larger storage capacities.

The multiplicity of solutions in non-homogeneous boundary value problems

Abstract: We use a method recently devised by Bolle to establish the existence of an infinite number of solutions for various non-homogeneous boundary value problems. In particular, we consider second order systems, Hamiltonian systems as well as semi-linear partial differential equations. The non-homogeneity can originate in the equation but also from the boundary conditions. The results are more satisfactory than those obtained by the standard “Perturbation from Symmetry” method that was developed – in various forms – in the early eighties by Bahri–Berestycki, Struwe and Rabinowitz.

Ekman layers of rotating fluids: The case of general initial data

Abstract: In this paper we describe the weak solutions of the Navier-Stokes equations with a large Coriolis term as the Rossby and the Ekman numbers go to zero in a special domain with various boundary conditions. This work extends the results (in the case of well-prepared initial data) in [19, 30]. © 2000 John Wiley & Sons, Inc.

Existence of neighbouring feasible trajectories: applications to dynamic programming for state constrained optimal control problems

Abstract: In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semi-continuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.

On the Pettis Integral of Closed Valued Multifunctions

Abstract: In this work, the study of Pettis integrability for multifunctions (alias set-valued maps), whose values are allowed to be unbounded, is initiated For this purpose, two notions of Pettis integrability, and of Pettis integral, are considered and compared The first notion is similar to that of the weak integral, already known for vector-valued functions, and is defined via support functions The second notion resembles the classical Aumann definition using integrable selections, but it involves the Pettis integrable selections rather than the Bochner integrable ones The above two integrals are shown to coincide in a quite general setting Several criteria for a multifunction to be Pettis integrable (in one sense or the other) are proved On the other hand, due to the possibility of infinite values for the support functions, we are led to introduce a more general notion of scalar integrability involving the negative part of these functions We compare the scalar integrability of a multifunction with that of its measurable selections We also provide some new results concerning multifunctions with bounded values and/or new proofs of already existing ones Examples are included to illustrate the results and to introduce open problems

Variational characterization for eigenvalues of Dirac operators

Abstract: In this paper we give two different variational characterizations for the eigenvalues of H+V where H denotes the free Dirac operator and V is a scalar potential The first one is a min-max involving a Rayleigh quotient The second one consists in minimizing an appropriate nonlinear functional Both methods can be applied to potentials which have singularities as strong as the Coulomb potential

Valued Tolerance and Decision Rules

Abstract: The concept of valuedtolerance is introducedas an extension of the usual concept of indiscernibility (which is a crisp equivalence relation) in rough sets theory. Some specific properties of the approach are discussed. Further on the problem of inducing rules is addressed. Properties of a "credibility degree" associated to each rule are analysed and its use in classification problems is discussed.

Local Solutions for Stochastic Navier Stokes Equations

Abstract: In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.

Numerical Schemes for Discontinuous Value Functions of Optimal Control

Abstract: In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.

A real‐world MCDA application: evaluating software

Abstract: A real-world multi-criteria decision aid (MCDA) application on software evaluation is presented in this paper. The decision process concerned a big Italian company faced with the management of a call for tenders for a very important software acquisition. The decision aiding process is extensively presented and discussed, mainly as far as its products are concerned, i.e. -the problem situation; -the problem formulation; -the evaluation model; -the final recommendation. The results of the experience are discussed using the comments of the client of the study

Optimality Conditions and Synthesis for the Minimum Time Problem

Abstract: We study the minimum time optimal control problem for a nonlinear system in R n with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis.

Generalization of the Principal Components Analysis to Histogram Data

Abstract: In this article we propose an algorithm for Principal Components Analysis when the variables are histogram type. This algorithm also works if the data table has variables of interval type and histogram type mixed. If all the variables are interval type it produces the same output as the one produced by the algorithm of the Centers Method propose in [5, Cazes, Chouakria, Diday and Schektman (1997)]. 1 The algorithm In this algorithm we use the idea proposed in [9, Diday (1998)]. We represent each histogram–individual by a succession of k interval–individuals (the first one included in the second one, the second one included in the third one and so on) where k is the maximum number of modalities taken by some variable in the input symbolic data table. Instead of representing the histograms in the factorial plane, we are going to represent the Empirical Distribution Function FY defined, in [3, Bock and Diday (2000)] associated with each histogram. In other words if we have an histogram variable Y on a set E = {a1, a2, . . .} of objects with domain Y represented by the mapping Y (a) = (U(a), πa), for a ∈ E, where πa is frequency distribution, then in the algorithm we will use the function F (x) = ∑ i / πi≤x πi instead of the histogram. Definition 1. Let X = (xij)i=1,2,...,m, j=1,2,...,n be a symbolic data table with variables type continuous, interval and histogram, and let be k = max{s, where s is the number of modalities of Y j , j = 1, 2, . . . , n} where Y j is a variable of histogram type1. We define the vector–succession of intervals associated with each cell of X as: 1 If all the variables are interval type then k = 1. 1. if xij = [a, b] then the vector–succession of intervals associated is: xij = 

Fluid-Structure Interaction: A Theoretical Point of View

Abstract: This paper deals with the mathematical and numerical analysis of fluid-structure interaction phenomena, and present some of the existence results that can be found on this subject. We explain the various approaches and review the technical tools required. In all cases we have a fluid interacting with a moving (rigid or deformable) structure. The fluid is supposed to be viscous (compressible or incompressible) and the fluid equations are set in an unknown, time dependent domain, determined by the structure deformations, itselves resulting from a stress applied by the fluid.

Asymptotic Problems and Compressible-Incompressible Limit

Abstract: This series of lectures is devoted to the study of some asymptotic problems in fluid mechanics and mainly to the study of the compressible-incompressible limit when the Mach number goes to zero or when the adiabatic constant γ goes to infinity.

The Bermuda Triangle: Weather, Electricity, and Insurance Derivatives

Abstract: Deregulation of electricity markets, well under way in the United States, has created an environment of severe competition for the U.S. utilities and gas producers, and will probably put European utilities under the same pressure once the Directives on gas and electricity deregulation become effective over the continent. This article offers a brief review of the development of several forms of weather, electricity, and insurance derivatives as well as the theoretical and mathematical basis for futures and option models on particular forms of these derivatives.

Securitization: The Transformation of Illiquid Financial Assets into Liquid Capital Market Securities Examples from the European Market

Abstract: Since the benefits a firm can derive from securitization are universal, the discussion of a market bounded by national borders is somewhat artificial unless the focus is on constraints particular to the country which promote or inhibit the use of securitization. With the exception of the United Kingdom, regulatory constraints have been an important factor in slowing the development of a European market for asset and mortgage backed securities. In addition to the regulatory hurdles, securitization in Europe has been inhibited by segmented corporate bond markets and the relatively slow development of money market savings vehicles for households. Liquidity across credit spectrums has been enhanced since the introduction of the Euro, as has been the competition for savings. European companies are developing the ability to securitize even if the technique is not yet being widely exploited. What is the European market for mortgage and asset backed securities? Does it include the U.S. credit card banks, Citicorp, Chase, MBNA, and First USA that have refinanced U.S. credit card receivables in European currencies and in Euro? Does it include GMAC which has structured Swiss Franc and Euro ABS backed by its U.S. dealer floor plan loans? Does it include Japanese banks that have refinanced Yen denominated leases with Euro and Swiss Franc ABS? Does it include Barclays' issue of $1 billion of ABS backed by sterling credit card receivables? Of course the answer is yes. Markets are defined by both the supply and demand sides. Our analysis focuses on the supply side of the domestic European market.

A Model Checking Method for Partially Symmetric Systems

Abstract: A new method of model checking is proposed based on the existence of symmetries in system. We show how to fully handle the partial symmetries of both properties and systems. Our method does not depend on a particular formalism and a priori can be applied to any one. Well-formed Petri Nets are used as an illustration.

Pricing Convexity Adjustment with Wiener Chaos

Abstract: This paper presents an approximated formula of the convexity adjustment of Constant Maturity Swap rates, using Wiener Chaos expansion, for multi-factor lognormal zero coupon models. We derive closed formulae for CMS bond and swap and apply results to various well-known one-factor models (Ho and Lee (1986), Amin and Jarrow (1992), Hull and White (1990), Mercurio and Moraleda (1996)). Quasi Monte Carlo simulations confirm the efficiency of the approximation. Its precision relies on the importance of second and higher order terms.

Master-Slave Strategy and Polynomial Approximation

Abstract: A lot of minimization covering problems on graphs consist in covering vertices or edges by subgraphs verifying a certain property. These problems can be seen as particular cases of set-covering. If the number of subgraphs is polynomial in the order n of the input-graph, then these problems can be approximated within logarithmic ratio by the classical greedy set-covering algorithm. We extend the class of problems approximable by this approach to covering problems where the number of candidate subgraphs is exponential in n, by revisiting an old technique called “master-slave” and extending it to weighted master or/and slave problems. Finally, we use the master-slave tool to prove some positive approximation results for two network-design and a VLSI-design graph-problems.

The software dimensions theory

Abstract: Since the early times, software academics and practitioners talk about a « crisis » in the software industry. Nevertheless, nowadays this crisis is more critical as organizations can not exist without operational software to support their production and decision-making processes. Solutions proposed to date, in order to deal with this software crisis, have partly failed on the one hand, because of the increasing complexity of software systems and on the other hand, because they don’t take into account all the aspects of software engineering: that means economical, technical, functional, structural as well as human and organizational aspects. This paper proposes a theory, called “software dimensions theory” which permits analyzing deeply the software crisis. In particular, this theory may be used to elaborate software development methodologies which permits coping with the effects of the software crisis. Our work rests on an organizational model based on the Leavitt model which takes into account behavioural aspects and impact of information technology on modern organizations. With the help of this model we determine ten software dimensions. Case studies, lessons learned and problems encountered while using the software dimensions theory are synthesized in the last part of this paper.