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Autor Yor, Marc |
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Título : Aspects of Brownian Motion Tipo de documento: documento electrónico Autores: Mansuy, Roger ; SpringerLink (Online service) ; Yor, Marc Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIV, 200 p Il.: online resource ISBN/ISSN/DL: 978-3-540-49966-4 Idioma : Inglés (eng) Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum. Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance Nota de contenido: The Gaussian space of BM -- The laws of some quadratic functionals of BM -- Squares of Bessel processes and Ray-Knight theorems for Brownian local times -- An explanation and some extensions of the Ciesielski-Taylor identities -- On the winding number of planar BM -- On some exponential functionals of Brownian motion and the problem of Asian options -- Some asymptotic laws for multidimensional BM -- Some extensions of Paul Lévy’s arc sine law for BM -- Further results about reflecting Brownian motion perturbed by its local time at 0 -- On principal values of Brownian and Bessel local times -- Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes En línea: http://dx.doi.org/10.1007/978-3-540-49966-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34314 Aspects of Brownian Motion [documento electrónico] / Mansuy, Roger ; SpringerLink (Online service) ; Yor, Marc . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - XIV, 200 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-540-49966-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum. Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance Nota de contenido: The Gaussian space of BM -- The laws of some quadratic functionals of BM -- Squares of Bessel processes and Ray-Knight theorems for Brownian local times -- An explanation and some extensions of the Ciesielski-Taylor identities -- On the winding number of planar BM -- On some exponential functionals of Brownian motion and the problem of Asian options -- Some asymptotic laws for multidimensional BM -- Some extensions of Paul Lévy’s arc sine law for BM -- Further results about reflecting Brownian motion perturbed by its local time at 0 -- On principal values of Brownian and Bessel local times -- Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes En línea: http://dx.doi.org/10.1007/978-3-540-49966-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34314 Ejemplares
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Título : Aspects of Mathematical Finance Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Yor, Marc Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Número de páginas: VIII, 80 p Il.: online resource ISBN/ISSN/DL: 978-3-540-75265-3 Idioma : Inglés (eng) Palabras clave: Mathematics Economics, Mathematical Public finance Quantitative Finance Economics Clasificación: 51 Matemáticas Resumen: Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes. The Ariadne’s thread leads the reader from Louis Bachelier’s thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavin’s stochastic calculus of variations. The book also features a description of the trainings of French financial analysts which will help them to become experts in these fast evolving mathematical techniques. The authors are: P. Barrieu, N. El Karoui, H. Föllmer, H. Geman, E. Gobet, G. Pagès, W. Schachermayer and M. Yor Nota de contenido: Introduction: Some Aspects of Financial Mathematics -- Financial Uncertainty, Risk Measures and Robust Preferences -- The Notion of Arbitrage and Free Lunch in Mathematical Finance -- Dynamic Financial Risk Management -- Stochastic Clock and Financial Markets -- Options and Partial Differential Equations -- Mathematics and Finance En línea: http://dx.doi.org/10.1007/978-3-540-75265-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34354 Aspects of Mathematical Finance [documento electrónico] / SpringerLink (Online service) ; Yor, Marc . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - VIII, 80 p : online resource.
ISBN : 978-3-540-75265-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Economics, Mathematical Public finance Quantitative Finance Economics Clasificación: 51 Matemáticas Resumen: Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes. The Ariadne’s thread leads the reader from Louis Bachelier’s thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavin’s stochastic calculus of variations. The book also features a description of the trainings of French financial analysts which will help them to become experts in these fast evolving mathematical techniques. The authors are: P. Barrieu, N. El Karoui, H. Föllmer, H. Geman, E. Gobet, G. Pagès, W. Schachermayer and M. Yor Nota de contenido: Introduction: Some Aspects of Financial Mathematics -- Financial Uncertainty, Risk Measures and Robust Preferences -- The Notion of Arbitrage and Free Lunch in Mathematical Finance -- Dynamic Financial Risk Management -- Stochastic Clock and Financial Markets -- Options and Partial Differential Equations -- Mathematics and Finance En línea: http://dx.doi.org/10.1007/978-3-540-75265-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34354 Ejemplares
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Título : Mathematical Methods for Financial Markets Tipo de documento: documento electrónico Autores: Jeanblanc, Monique ; SpringerLink (Online service) ; Yor, Marc ; Chesney, Marc Editorial: London : Springer London Fecha de publicación: 2009 Colección: Springer Finance, ISSN 1616-0533 Número de páginas: XXVI, 732 p. 9 illus Il.: online resource ISBN/ISSN/DL: 978-1-84628-737-4 Idioma : Inglés (eng) Palabras clave: Finance Applied mathematics Engineering Economics, Mathematical Probabilities Public finance Economics Applications of Mathematics Quantitative Finance, general Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. The subject draws upon quite difficult results from the theory of stochastic processes, stochastic calculus and differential equations, among others, which can be daunting for the beginning researcher. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The authors proceed by successive generalisations with increasing complexity assuming some basic knowledge of probability theory. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice Nota de contenido: Continuous Path Processes -- Continuous-Path Random Processes: Mathematical Prerequisites -- Basic Concepts and Examples in Finance -- Hitting Times: A Mix of Mathematics and Finance -- Complements on Brownian Motion -- Complements on Continuous Path Processes -- A Special Family of Diffusions: Bessel Processes -- Jump Processes -- Default Risk: An Enlargement of Filtration Approach -- Poisson Processes and Ruin Theory -- General Processes: Mathematical Facts -- Mixed Processes -- Lévy Processes En línea: http://dx.doi.org/10.1007/978-1-84628-737-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33976 Mathematical Methods for Financial Markets [documento electrónico] / Jeanblanc, Monique ; SpringerLink (Online service) ; Yor, Marc ; Chesney, Marc . - London : Springer London, 2009 . - XXVI, 732 p. 9 illus : online resource. - (Springer Finance, ISSN 1616-0533) .
ISBN : 978-1-84628-737-4
Idioma : Inglés (eng)
Palabras clave: Finance Applied mathematics Engineering Economics, Mathematical Probabilities Public finance Economics Applications of Mathematics Quantitative Finance, general Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. The subject draws upon quite difficult results from the theory of stochastic processes, stochastic calculus and differential equations, among others, which can be daunting for the beginning researcher. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The authors proceed by successive generalisations with increasing complexity assuming some basic knowledge of probability theory. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice Nota de contenido: Continuous Path Processes -- Continuous-Path Random Processes: Mathematical Prerequisites -- Basic Concepts and Examples in Finance -- Hitting Times: A Mix of Mathematics and Finance -- Complements on Brownian Motion -- Complements on Continuous Path Processes -- A Special Family of Diffusions: Bessel Processes -- Jump Processes -- Default Risk: An Enlargement of Filtration Approach -- Poisson Processes and Ruin Theory -- General Processes: Mathematical Facts -- Mixed Processes -- Lévy Processes En línea: http://dx.doi.org/10.1007/978-1-84628-737-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33976 Ejemplares
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Título : Option Prices as Probabilities : A New Look at Generalized Black-Scholes Formulae Tipo de documento: documento electrónico Autores: Profeta, Cristophe ; SpringerLink (Online service) ; Roynette, Bernard ; Yor, Marc Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2010 Colección: Springer Finance, ISSN 1616-0533 Número de páginas: XXI, 270 p. 3 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-10395-7 Idioma : Inglés (eng) Palabras clave: Mathematics Economics, Mathematical Probabilities Probability Theory and Stochastic Processes Quantitative Finance Clasificación: 51 Matemáticas Resumen: The Black-Scholes formula plays a central role in Mathematical Finance; it gives the right price at which buyer and seller can agree with, in the geometric Brownian framework, when strike K and maturity T are given. This yields an explicit well-known formula, obtained by Black and Scholes in 1973. The present volume gives another representation of this formula in terms of Brownian last passages times, which, to our knowledge, has never been made in this sense. The volume is devoted to various extensions and discussions of features and quantities stemming from the last passages times representation in the Brownian case such as: past-future martingales, last passage times up to a finite horizon, pseudo-inverses of processes... They are developed in eight chapters, with complements, appendices and exercises Nota de contenido: Reading the Black-Scholes Formula in Terms of First and Last Passage Times -- Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times -- Representation of some particular Azéma supermartingales -- An Interesting Family of Black-Scholes Perpetuities -- Study of Last Passage Times up to a Finite Horizon -- Put Option as Joint Distribution Function in Strike and Maturity -- Existence and Properties of Pseudo-Inverses for Bessel and Related Processes -- Existence of Pseudo-Inverses for Diffusions En línea: http://dx.doi.org/10.1007/978-3-642-10395-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33732 Option Prices as Probabilities : A New Look at Generalized Black-Scholes Formulae [documento electrónico] / Profeta, Cristophe ; SpringerLink (Online service) ; Roynette, Bernard ; Yor, Marc . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2010 . - XXI, 270 p. 3 illus : online resource. - (Springer Finance, ISSN 1616-0533) .
ISBN : 978-3-642-10395-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Economics, Mathematical Probabilities Probability Theory and Stochastic Processes Quantitative Finance Clasificación: 51 Matemáticas Resumen: The Black-Scholes formula plays a central role in Mathematical Finance; it gives the right price at which buyer and seller can agree with, in the geometric Brownian framework, when strike K and maturity T are given. This yields an explicit well-known formula, obtained by Black and Scholes in 1973. The present volume gives another representation of this formula in terms of Brownian last passages times, which, to our knowledge, has never been made in this sense. The volume is devoted to various extensions and discussions of features and quantities stemming from the last passages times representation in the Brownian case such as: past-future martingales, last passage times up to a finite horizon, pseudo-inverses of processes... They are developed in eight chapters, with complements, appendices and exercises Nota de contenido: Reading the Black-Scholes Formula in Terms of First and Last Passage Times -- Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times -- Representation of some particular Azéma supermartingales -- An Interesting Family of Black-Scholes Perpetuities -- Study of Last Passage Times up to a Finite Horizon -- Put Option as Joint Distribution Function in Strike and Maturity -- Existence and Properties of Pseudo-Inverses for Bessel and Related Processes -- Existence of Pseudo-Inverses for Diffusions En línea: http://dx.doi.org/10.1007/978-3-642-10395-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33732 Ejemplares
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Título : Peacocks and Associated Martingales, with Explicit Constructions Tipo de documento: documento electrónico Autores: Hirsch, Francis ; SpringerLink (Online service) ; Profeta, Christophe ; Roynette, Bernard ; Yor, Marc Editorial: Milano : Springer Milan Fecha de publicación: 2011 Colección: B&SS — Bocconi & Springer Series, ISSN 2039-1471 Número de páginas: XXXII, 388 p Il.: online resource ISBN/ISSN/DL: 978-88-470-1908-9 Idioma : Inglés (eng) Palabras clave: Mathematics Economics, Mathematical Probabilities Probability Theory and Stochastic Processes Quantitative Finance Clasificación: 51 Matemáticas Resumen: We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings… They are developed in eight chapters, with about a hundred of exercises Nota de contenido: Some Examples of Peacocks -- The Sheet Method -- The Time Reversal Method -- The Time Inversion Method -- The Sato Process Method -- The Stochastic Differential Equation Method -- The Skorokhod Embedding (SE) Method. Comparison of Multidimensional Marginals En línea: http://dx.doi.org/10.1007/978-88-470-1908-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33473 Peacocks and Associated Martingales, with Explicit Constructions [documento electrónico] / Hirsch, Francis ; SpringerLink (Online service) ; Profeta, Christophe ; Roynette, Bernard ; Yor, Marc . - Milano : Springer Milan, 2011 . - XXXII, 388 p : online resource. - (B&SS — Bocconi & Springer Series, ISSN 2039-1471) .
ISBN : 978-88-470-1908-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Economics, Mathematical Probabilities Probability Theory and Stochastic Processes Quantitative Finance Clasificación: 51 Matemáticas Resumen: We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings… They are developed in eight chapters, with about a hundred of exercises Nota de contenido: Some Examples of Peacocks -- The Sheet Method -- The Time Reversal Method -- The Time Inversion Method -- The Sato Process Method -- The Stochastic Differential Equation Method -- The Skorokhod Embedding (SE) Method. Comparison of Multidimensional Marginals En línea: http://dx.doi.org/10.1007/978-88-470-1908-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33473 Ejemplares
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