# Patras, Frédéric

Overview
Works: 21 works in 64 publications in 3 languages and 1,182 library holdings History Author, Thesis advisor, 956, Editor, Opponent, 958 HG6024.U6, 332.6457
Publication Timeline
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Most widely held works by Frédéric Patras
Credit risk frontiers : subprime crisis, pricing and hedging, CVA, MBS, ratings, and liquidity by Tomasz R Bielecki( )

16 editions published between 2011 and 2013 in English and held by 492 WorldCat member libraries worldwide

"A timely guide to understanding and implementing credit derivatives Credit derivatives are here to stay and will continue to play a role in finance in the future. But what will that role be? What issues and challenges should be addressed? And what lessons can be learned from the credit mess? Credit Risk Frontiers offers answers to these and other questions by presenting the latest research in this field and addressing important issues exposed by the financial crisis. It covers this subject from a real world perspective, tackling issues such as liquidity, poor data, and credit spreads, as well as the latest innovations in portfolio products and hedging and risk management techniques. Provides a coherent presentation of recent advances in the theory and practice of credit derivatives. Takes into account the new products and risk requirements of a post financial crisis world. Contains information regarding various aspects of the credit derivative market as well as cutting edge research regarding those aspects. If you want to gain a better understanding of how credit derivatives can help your trading or investing endeavors, then Credit Risk Frontiers is a book you need to read."--
Rediscovering phenomenology : phenomenological essays on mathematical beings, physical reality, perception and consciousness by Luciano Boi( )

15 editions published in 2007 in English and held by 484 WorldCat member libraries worldwide

Beyond their remarkable technical accomplishments, the new directions taken by the sciences in recent decades call for renewal of their epistemological basis. The purpose of this book is to show that Husserl??'s transcendental phenomenology, if properly re-examined, provides the required framework for such an epistemology. This re-examination is both critical and constructive. (i) The absolute subjectivization or the full naturalization of consciousness must be rejected. (ii) The necessarily transcendental character of phenomenology is put to work in the search for a systematic connection betw
La pensée mathématique contemporaine by Frédéric Patras( Book )

8 editions published between 2001 and 2017 in French and Italian and held by 104 WorldCat member libraries worldwide

Pour comprendre le cheminement de la mathématique contemporaine, son affranchissement progressif des mots d'ordre des "maths modernes" et les voies ouvertes aujourd'hui, il faut d'abord déconstruire une histoire officielle réductrice. Au 19e et au début du 20e siècle une unité de la pensée mathématique s'est affirmée, qui dépassait les voies épistémologiques étroites du structuralisme, ceci dans les oeuvres de mathématiciens tels Galois ou Hilbert ou Weyl. C'est cette tradition de pensée accompagnée d'une exigence philosophique, tradition de savants et non de purs scientifiques, que la modernité nous apprend à faire revivre à travers les oeuvres d'Alexandre Grothendieck ou dans l'aristotélisme d'un René Thom
La possibilité des nombres by Frédéric Patras( Book )

5 editions published between 2014 and 2018 in French and held by 73 WorldCat member libraries worldwide

Les nombres sont des entités si familières, d'un emploi si quotidien, qu'il paraît inutile de s'attarder sur les modalités de leur existence. De Thalès et Pythagore à nos jours, l'histoire n'aura pourtant eu de cesse d'établir que nous ne comprenons jamais que de façon incomplète et insatisfaisante leur nature. La pluralité des points de vue possibles pour en traiter est étonnante, et sans cesse renouvelée. C'est de cette variété surprenante, mais aussi de la beauté et de la profondeur des analyses et des œuvres qui lui sont sous-jacentes, que La Possibilité des nombres cherche à rendre compte
Il pensiero matematico contemporaneo by Frédéric Patras( Book )

2 editions published in 2006 in Italian and held by 7 WorldCat member libraries worldwide

Homotheties simpliciales by Frederic Patras( Book )

2 editions published in 1992 in French and held by 7 WorldCat member libraries worldwide

Algèbres de Hopf combinatoires by Rémi Maurice( )

1 edition published in 2013 in French and held by 2 WorldCat member libraries worldwide

This thesis is in the field of algebraic combinatorics. In other words, the idea is to use algebraic structures, in this case of combinatorial Hopf algebras, to better study and understand the combinatorial objects and algorithms for composition and decomposition about these objects. This research is based on the construction and study of algebraic structure of combinatorial objects generalizing permutations. After recalling the background and notations of various objects involved in this research, we propose, in the second part, the study of the Hopf algebra introduced by Aguiar and Orellana based on uniform block permutations. By focusing on a description of these objects via well-known objects, permutations and set partitions, we propose a polynomial realization and an easier study of this algebra. The third section considers a second generalization interpreting permutations as matrices. We define and then study the families of square matrices on which we define algorithms for composition and decomposition. The fourth part deals with alternating sign matrices. Having defined the Hopf algebra of these matrices, we study the statistics and the behavior of the algebraic structure with these statistics. All these chapters rely heavily on computer exploration, and is the subject of an implementation using Sage software. This last chapter is dedicated to the discovery and manipulation of algebraic structures on Sage. We conclude by explaining the improvements to the study of algebraic structure through the Sage software
Sur la cohomologie des algèbres triangulaires et des algèbres de diagrammes by Sophie Dourlens( Book )

1 edition published in 2004 in French and held by 1 WorldCat member library worldwide

In the fist part of this thesis we generalize a result of Cibils : we construct a spectral sequence converging to the Hochschild cohomology of a triangular algebra, by using its quiver. We describe the terms and the differentials at the first level. We give some examples of use of this spectral sequence, by refinding formulas for the dimension of cohomologie groups of (possibly truncated) quiver algebras, for quivers without oriented cycles. In the second part we prove that a relative Hochschild cohomologie of the algebra associated with a diagram of commutative algebras over a finite category of the algebra associated with a diagram of commutative algebras over a finite category has a direct sum decomposition, induced by the action of the Eulerian idempotents. This result generalizes the Hodge-type decomposition of the cohomologie of a commutative algebra, obtained by Gerstenhaber and Schack (and others). In the thirs part we build a class of posets whose Hochschild homology of incidence algebras satisties an analog of the Poincaré duality. The fundamental notion to construct these "Poincaré duality posets" is one of CW-post defined by Björner. We establish a link between Poincarré duality posets and compact orientable manifolds
Deux exemples d'algèbres de Hopf d'extraction-contraction : mots tassés et diagrammes de dissection by Cécile Mammez( )

1 edition published in 2017 in French and held by 1 WorldCat member library worldwide

This thesis deals with the study of combinatorics of two Hopf algebras. The first one is the packed words Hopf algebra WMAT introduced by Duchamp, Hoang-Nghia, and Tanasa who wanted to build a coalgebra model for packed words by using a selection-quotient process. We describe certain sub-objects or quotient objects as well as maps to other Hopf algebras. We consider first a Hopf algebra of permutations. Its graded dual has a block deconcatenation coproduct and double shuffle product. The double shuffle product is commutative so the Hopf algebra is different from the Malvenuto and Reutenauer one. We analyze then the Hopf algebra generated by packed words looking like x₁...x₁. This Hopf algebra and non commutative symmetric functions are isomorphic. So its graded dual and quasi-symmetric functions are isomorphic too. Finally we consider a Hopf algebra of compositions an give its interpretation in terms of a semi-direct coproduct structure. The second objet we study is the Hopf algebra of dissection diagrams HD introduced by Dupont in number theory. We study the cofreedom problem. We can't conclude with homogeneous primitive elements of degree 3. With the degree 5 case, we can say that is not cofree with the parameter -1. We study the pre-Lie algebra structure of HD's graded dual too. We consider in particular the sup-pre-Lie algebra generated by the dissection diagram of degree 1. It is not a free pre-Lie algebra
Bases de monômes dans les algèbres pré-Lie libres et applications by Mahdi Jasim Hasan Al-Kaabi( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Dans cette thèse, nous étudions le concept d'algèbre pré-Lie libre engendrée par un ensemble (non-vide). Nous rappelons la construction par A. Agrachev et R. Gamkrelidze des bases de monômes dans les algèbres pré-Lie libres. Nous décrivons la matrice des vecteurs d'une base de monômes en termes de la base d'arbres enracinés exposée par F. Chapoton et M. Livernet. Nous montrons que cette matrice est unipotente et trouvons une expression explicite pour les coefficients de cette matrice, en adaptant une procédure suggérée par K. Ebrahimi-Fard et D. Manchon pour l'algèbre magmatique libre. Nous construisons une structure d'algèbre pré-Lie sur l'algèbre de Lie libre $\mathcal{L}$(E) engendrée par un ensemble E, donnant une présentation explicite de $\mathcal{L}$(E) comme quotient de l'algèbre pré-Lie libre $\mathcal{T}$^E, engendrée par les arbres enracinés (non-planaires) E-décorés, par un certain idéal I. Nous étudions les bases de Gröbner pour les algèbres de Lie libres dans une présentation à l'aide d'arbres. Nous décomposons la base d'arbres enracinés planaires E-décorés en deux parties O(J) et $\mathcal{T}$(J), où J est l'idéal définissant $\mathcal{L}$(E) comme quotient de l'algèbre magmatique libre engendrée par E. Ici, $\mathcal{T}$(J) est l'ensemble des termes maximaux des éléments de J, et son complément O(J) définit alors une base de $\mathcal{L}$(E). Nous obtenons un des résultats importants de cette thèse (Théorème 3.12) sur la description de l'ensemble O(J) en termes d'arbres. Nous décrivons des bases de monômes pour l'algèbre pré-Lie (respectivement l'algèbre de Lie libre) $\mathcal{L}$(E), en utilisant les procédures de bases de Gröbner et la base de monômes pour l'algèbre pré-Lie libre obtenue dans le Chapitre 2. Enfin, nous étudions les développements de Magnus classique et pré-Lie, discutant comment nous pouvons trouver une formule de récurrence pour le cas pré-Lie qui intègre déjà l'identité pré-Lie. Nous donnons une vision combinatoire d'une méthode numérique proposée par S. Blanes, F. Casas, et J. Ros, sur une écriture du développement de Magnus classique, utilisant la structure pré-Lie de $\mathcal{L}$(E)
Cochain algebras of mapping spaces and finite group actions by Frédéric Patras( Book )

1 edition published in 2002 in English and held by 1 WorldCat member library worldwide

Coalescent tree based functional representations for some Feynman-Kac particle models( Book )

1 edition published in 2006 in English and held by 1 WorldCat member library worldwide

Flows and stochastic Taylor series in Itô calculus( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Abstract: For general stochastic systems driven by continuous semimartingales an explicit formula for the logarithm of the Itô flow map is given. The computation relies on the lift to quasi-shuffle algebras of formulas involving products of Itô integrals of semimartingales. Whereas the Chen–Strichartz formula computing the logarithm of the Stratonovich flow map is classically expanded as a formal sum indexed by permutations, the analogous formula in Itô calculus is naturally indexed by surjections. This reflects the change of algebraic background involved in the transition between the two integration theories. Lastly, we extend our formula for the quasi-shuffle Chen–Strichartz series for the logarithm of the flow map to the non-commutative case. For linear matrix-valued SDEs driven by arbitrary semimartingales we obtain a similar formula
Rota-Baxter algebras and new combinatorial identities( )

1 edition published in 2007 in English and held by 1 WorldCat member library worldwide

Rota-Baxter algebras and new combinatorial identities by Kurusch Ebrahimi-Fard( Book )

1 edition published in 2007 in English and held by 1 WorldCat member library worldwide

La naissance de la cohomologie des groupes by Nicolas Basbois( Book )

1 edition published in 2009 in French and held by 1 WorldCat member library worldwide

The goal of this thesis is the historical study of the genesis of group cohomology, a theory that came up during the nineteen-forties. It is an algebraic theory in the sense that it gives results on groups and it is as well a topologic one because of the methods it involves. The present work analyses how topology and algebra interpenetrated each other to give birth to this abstract and elaborate theory, by putting into perspective this phenomenon with respect to more global ones like the birth and the rise of modern algebra. Namely we discuss the influence of Emmy Noether in the algebraization of topology and the respective motivations of Heinz Hopf and Eilenberg & Mac Lane that led them to the development of group homology. A meticulous analysis of several seminal articles - due to the authors cited above and others including Schur, Vietoris and Eckmann - enables to highlight the fact that the will to answer specific mathematical problems was perhaps more propulsive in the emergence of this architectonic theory that group cohomology is, than great guiding ideas elaborated in the framework of structural representations of mathematics
Linéarisation de structures algébriques à l'aide d'opérades et de foncteurs polynomiaux : Les équivalences quadratiques et la formule de Baker-Campbell-Hausdorff pour les variétés 2-nilpotentes by Thibault Defourneau( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Le travail de thèse contribue à établir des liens entre structures algébriques non-linéaires, décrites par des théories algébriques, et des structures algébriques linéaires, encodées par des algèbres sur une opérade linéaire. Pour les théories algébriques dont les modèles forment une catégorie semi-abélienne (ce qui inclut la plupart des structures intéressantes), un tel lien a été exhibé récemment par M. Hartl, au niveau des objets gradués associés à une nouvelle notion de suite centrale descendante des modèles d'une théorie donnée : il s'avère qu'ils ont une structure naturelle d'algèbre graduée sur une certaine opérade de groupes abéliens associée à la théorie. Le sujet de thèse s'inscrit dans le projet d'étendre ce lien au niveau global, c'est-à-dire d'établir des correspondances du type Mal'cev et Lazard dans le cas des groupes, à savoir entre les modèles nilpotents suffisamment radicables et les algèbres nilpotentes sur l'opérade linéaire correspondante (après tensorisation avec un sous-anneau des rationnels approprié). Ces correspondances jouent un rôle fondamental en théorie des groupes et commencent à faire leurs preuves en théorie des loops grâce au développement plus récent d'une théorie de Lie non-associative; on peut s'attendre à ce qu'il en soit de même dans un contexte plus général. Il est important de noter qu'aussi bien dans les correspondances classiques de Mal'cev et Lazard que dans leurs généralisations à des variétés multiples de loops (Moufang, Bruck, Bol etc.), le passage des algèbres (de Lie, de Mal'cev etc.) appropriées aux objets non-linéaires (groupes, voire loops) qui leur correspondent, est donné par une formule de Baker-Campbell-Hausdorff appropriée, déduite d'une étude de fonctions exponentielles et logarithmes. Dans la thèse, une nouvelle approche est développée pour construire une correspondance (en fait, une équivalence de catégories) du type Lazard entre une variété (dite aussi catégorie algébrique) 2- nilpotente 2-radicable (dans un sens approprié) C donnée et les algèbres sur une opérade symétrique unitaire linéaire et 2-nilpotente AbOp(C) dépendant de la variété, vivant dans la catégorie monoïdale des Z[1/2]-modules à gauche. L'anneau de fraction Z[1/2] apparaît car notre définition de 2-divisibilité d'objets de C se traduit par la condition de 2-divisibilité classique sur le premier terme de l'opérade. L'équivalence de type Lazard se construit grâce à la théorie des foncteurs polynomiaux (plus précisément quadratiques) et à la notion d'extension linéaire de catégories. L'idée principale est de chercher une équivalence quadratique (i.e un foncteur quadratique qui est une équivalence de catégories) entre une variété semi-abélienne 2-nilpotente 2-radicable donnée C et la catégorie des algèbres sur AbOp(C), que nous appellerons le foncteur de Lazard. La nouveauté principale de cette approche est de ne pas construire ce foncteur explicitement sur tous les objets et les morphismes, en utilisant une formule de BCH établie au préalable; mais au contraire de construire l'"ADN" du foncteur de Lazard, c'est-à-dire un ensemble de données minimales le caractérisant étudié dans ce travail de thèse, et d'en déduire une formule de type BCH dans notre contexte. Cette démarche devrait pouvoir se généraliser et ainsi fournir une approche nouvelle et intéressante même de la formule BCH classique
Credit Risk Frontiers: Subprime Crisis, Pricing and Hedging, CVA, MBS, Rati by Tomasz Bielecki( Book )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

Estimation des modèles à volatilité stochastique par filtrage et déconvolution by Salima El Kolei( Book )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

This thesis deals with the estimation of the state and/or the parameters of state-space models. The motivations come from financial applications, namely, from the estimation of the stochastic volatility and the parameters of its dynamics. Here, we consider two models : the Taylor SV model and the Heston model. After presenting the filtering methods, we propose a new approach of M-estimation based on a déconvolution strategy for linear state space models. We show that this method leads to a consistent and asymptotically normal estimator with an explicit variance, allowing constructing asymptotic confidence interval in practice. For the SV model, a thorough comparison with filtering methods and other classical methods is given on simulated and real data. This study shows the performance of our new approach. The Heston model is an example of complex state space models and, due to the nonlinearity, we cannot apply our approach. Nevertheless, filtering methods can be used for this model and we show how the filters update the estimation of the volatility and the parameters thanks to the observation of option prices. This illustrates the flexibility of these methods. Finally, we analyze the model risk induces by an error in the estimation of the parameters. Our objective consists in understanding the behavior of the filtering methods when the model is not well parameterized. A theoretical analysis consists in isolating the model risk due to the uncertainty of the parameters from the error of estimation for linear (and weakly nonlinear) models. An application of this result is given for the Heston model
Rediscovering Phenomenology Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness( )

2 editions published in 2007 in English and held by 1 WorldCat member library worldwide

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Alternative Names
Frédéric Patras born 1967; VIAF 46974384

Patras, Frederic

Languages
English (42)

French (17)

Italian (4)