Synergy Modelling and Financial Valuation : the contribution of Fuzzy Integrals.

Les méthodes d’évaluation financière utilisent des opérateurs d’agrégation reposant sur les propriétés d’additivité (sommations, intégrales de Lebesgue). De ce fait, elles occultent les phénomènes de renforcement et de synergie (ou de redondance) qui peuvent exister entre les éléments d’un ensemble organisé. C’est particulièrement le cas en ce qui concerne le problème d’évaluation financière du patrimoine d’une entreprise : en effet, en pratique, il est souvent mis en évidence une importante différence de valorisation entre l’approche « valeur de la somme des éléments » (privilégiant le point de vue financier) et l’approche « somme de la valeur des différents éléments » (privilégiant le point de vue comptable). Les possibilités offertes par des opérateurs d’agrégation comme les intégrales floues (Sugeno, Grabisch, Choquet) permettent, au plan théorique, de modéliser l’effet de synergie. La présente étude se propose de valider empiriquement les modalités d’implémentation opérationnelle de ce modèle à partir d’un échantillon d’entreprises cotées ayant fait l’objet d’une évaluation lors d’une OPA.Financial valuation methods use additive aggregation operators. But a patrimony should be regarded as an organized set, and additivity makes it impossible for these aggregation operators to formalize such phenomena as synergy or mutual inhibition between the patrimony’s components. This paper considers the application of fuzzy measure and fuzzy integrals (Sugeno, Grabisch, Choquet) to financial valuation. More specifically, we show how integration with respect to a non additive measure can be used to handle positive or negative synergy in value construction.Fuzzy measure; Fuzzy integral; Aggregation operator; Synergy; Financial valuation;

Intangibles mismeasurements, synergy, and accounting numbers : a note.

For the last two decades, authors (e.g. Ohlson, 1995; Lev, 2000, 2001) have regularly pointed out the enforcement of limitations by traditional accounting frameworks on financial reporting informativeness. Consistent with this claim, it has been then argued that accounting finds one of its major limits in not allowing for direct recognition of synergy occurring amongst the firm intangible and tangible items (Casta, 1994; Casta & Lesage, 2001). Although the firm synergy phenomenon has been widely documented in the recent accounting literature (see for instance, Hand & Lev, 2004; Lev, 2001) research hitherto has failed to provide a clear approach to assess directly and account for such a henceforth fundamental corporate factor. The objective of this paper is to raise and examine, but not address exhaustively, the specific issues induced by modelling the synergy occurring amongst the firm assets whilst pointing out the limits of traditional accounting valuation tools. Since financial accounting valuation methods are mostly based on the mathematical property of additivity, and consequently may occult the perspective of regarding the firm as an organized set of assets, we propose an alternative valuation approach based on non-additive measures issued from the Choquet's (1953) and Sugeno's (1997) framework. More precisely, we show how this integration technique with respect to a non-additive measure can be used to cope with either positive or negative synergy in a firm value-building process and then discuss its potential future implications for financial reporting.Financial reporting; accounting goodwill; assets synergy; non-additive measures; Choquet’s framework;

До відома авторів журналу «Питання історії науки і техніки»

Bry Xavier, Antoine Philippe.- Exploring the explanatory: an application to event history data This article presents an empirical plugging of factor analysis and generalized linear regression (logistic regression, Cox models, ...)■ We show that this combination can facilitate the exploration of complex data such as that on event histories (time-varying, censored) for modelling purposes. By combining a regression method with a new type of factor analysis — Thematic Components Analysis — we show how an explanatory conceptual model for the data can be included from the start of the exploratory phase. This method is then applied to an analysis of the divorce behaviour of men in Dakar, and used to give a simple illustration of each methodological point discussed.Bry Xavier, Antoine Philippe.- Explorer 1'explicatif : application à l'analyse biographique Ce travail relie de façon empirique analyses factorielles et régressions linéaires généralisées (régression logistique, de Cox, etc.). Nous montrons comment ce couplage permet de faciliter l'exploration de données complexes comme les données biographiques (variant dans le temps, incomplètement observées) en vue de leur modélisation. Nous associons une méthode de régression à une nouvelle méthode factorielle - l'analyse en composantes thématiques - qui permet de tenir compte, dès le départ, d'un modèle conceptuel explicatif des données. Cette méthode est ensuite appliquée à l'analyse du divorce des hommes à Dakar, ce qui permet d'illustrer simplement chaque point méthodologique abordé.Bry Xavier, Antoine Philippe.- Analizar las causas: aplicación al análisis biográfico En este articulo se relacionan de modo empírico análisis factoriales y regresiones linea- les generalizadas (regresión logística, de Сох, etc.). También se muestra como tal conexión facilita el análisis de datos complejos taies como los datos biográficos (que varian a través del tiempo y cuya observación es incompleta) y su modelización. Asociamos un método de regresión a un nuevo método factorial - el análisis de componentes temáticos - que permite tomar en cuenta, desde el principio, un modelo conceptual explicativo de los datos. A continuación aplicamos este método al análisis del divorcio masculino en Dakar para ilustrar de forma simple cada paso metodológico.Bry X., Antoine P. Exploring the explanatory: an application to event history data. In: Population (English edition), 59ᵉ année, n°6, 2004. pp. 795-830

A multiple covariance approach to PLS regression with several predictor groups: Structural Equation Exploratory Regression

A variable group Y is assumed to depend upon R thematic variable groups X 1, >..., X R . We assume that components in Y depend linearly upon components in the Xr's. In this work, we propose a multiple covariance criterion which extends that of PLS regression to this multiple predictor groups situation. On this criterion, we build a PLS-type exploratory method - Structural Equation Exploratory Regression (SEER) - that allows to simultaneously perform dimension reduction in groups and investigate the linear model of the components. SEER uses the multidimensional structure of each group. An application example is given

Supervised-Component versus PLS regression. The case of GLMMs with autoregressive random effect

International audienc

Component-based regularisation of multivariate generalised linear mixed models

International audienceWe address the component-based regularisation of a multivariate Generalised Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory variables, a set A of additional explanatory variables, and random effects to introduce the within-group dependence of observations. Variables in X are assumed many and redundant so that regression demands regularisation. This is not the case for A, which contains few and selected variables. Regularisation is performed building an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X. To estimate the model, we propose to maximise a criterion specific to the Supervised Component-based Generalised Linear Regression (SCGLR) within an adaptation of Schall's algorithm. This extension of SCGLR is tested on both simulated and real grouped data, and compared to ridge and LASSO regularisations. Supplementary material for this article is available online