Paul Malliavin's Books

Stochastic Calculus of Variations in Mathematical Finance

By: Paul Malliavin,Anton Thalmaier

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Stochastic Calculus of Variations in Mathematical Finance

By: Paul Malliavin,Anton Thalmaier

Highly esteemed author Topics covered are relevant and timely

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Page Count

148

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Springer Science & Business Media

Published Date

ISBN 10

3540307990

ISBN 13

9783540307990

Stochastic Analysis

By: Paul Malliavin

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In 5 independent sections, this book accounts recent main developments of stochastic analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

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346

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Springer

Published Date

ISBN 10

3642150748

ISBN 13

9783642150746

Integration and Probability

By: Paul Malliavin

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Integration and Probability

By: Paul Malliavin

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

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341

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Springer Science & Business Media

Published Date

ISBN 10

1461242029

ISBN 13

9781461242024

Monte Carlo Methods in Financial Engineering

By: Paul Glasserman

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Monte Carlo Methods in Financial Engineering

By: Paul Glasserman

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

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Page Count

603

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Springer Science & Business Media

Published Date

ISBN 10

0387216170

ISBN 13

9780387216171

Mathematical Analysis during the 20th Century

By: Jean-Paul Pier

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Mathematical Analysis during the 20th Century

By: Jean-Paul Pier

For several centuries, analysis has been one of the most prestigious and important subjects in mathematics. The present book sets off by tracing the evolution of mathematical analysis, and then endeavours to understand the developments of main trends, problems, and conjectures. It features chapters on general topology, 'classical' integration and measure theory, functional analysis, harmonic analysis and Lie groups, theory of functions and analytic geometry, differential and partial differential equations, topological and differential geometry. The ubiquitous presence of analysis also requires the consideration of related topics such as probability theory or algebraic geometry. Each chapter features a comprehensive first part on developments during the period 1900-1950, and then provides outlooks on representative achievements during the later part of the century. The book provides many original quotations from outstanding mathematicians as well as an extensive bibliography of the seminal publications. It will be an interesting and useful reference work for graduate students, lecturers, and all professional mathematicians and other scientists with an interest in the history of mathematics.

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Page Count

440

Publisher

OUP Oxford

Published Date

ISBN 10

0191544949

ISBN 13

9780191544941

Stochastic Models for Prices Dynamics in Energy and Commodity Markets

An Infinite-Dimensional Perspective

By: Fred Espen Benth,Paul Krühner

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Stochastic Models for Prices Dynamics in Energy and Commodity Markets

An Infinite-Dimensional Perspective

By: Fred Espen Benth,Paul Krühner

This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets. In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity 'delta' expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing. This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.

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Page Count

250

Publisher

Springer Nature

Published Date

ISBN 10

3031403673

ISBN 13

9783031403675

Geometric Analysis and PDEs

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 11-16, 2007

By: Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang

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Geometric Analysis and PDEs

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 11-16, 2007

By: Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

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Page Count

296

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642016731

ISBN 13

9783642016738

Quantum Probability for Probabilists

By: Paul-Andre Meyer

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Quantum Probability for Probabilists

By: Paul-Andre Meyer

These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.

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Page Count

301

Publisher

Springer

Published Date

ISBN 10

3662215586

ISBN 13

9783662215586

Exotic Option Pricing and Advanced Lévy Models

By: Andreas Kyprianou,Wim Schoutens,Paul Wilmott

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Exotic Option Pricing and Advanced Lévy Models

By: Andreas Kyprianou,Wim Schoutens,Paul Wilmott

Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

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344

Publisher

John Wiley & Sons

Published Date

ISBN 10

0470017201

ISBN 13

9780470017203

Fukaya Categories and Picard-Lefschetz Theory

By: Paul Seidel

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Fukaya Categories and Picard-Lefschetz Theory

By: Paul Seidel

The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

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340

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190639

ISBN 13

9783037190630

Stochastic Models for Time Series

By: Paul Doukhan

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Stochastic Models for Time Series

By: Paul Doukhan

This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series.

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322

Publisher

Springer

Published Date

ISBN 10

3319769383

ISBN 13

9783319769387

The Logarithmic Integral

By: Paul Koosis

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The Logarithmic Integral

By: Paul Koosis

Self-contained study of real and complex analysis bringing together many separate parts of this subject.

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628

Publisher

Cambridge University Press

Published Date

ISBN 10

0521596726

ISBN 13

9780521596725

Harmonic Function Theory

By: Sheldon Axler,Paul Bourdon,Ramey Wade

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Harmonic Function Theory

By: Sheldon Axler,Paul Bourdon,Ramey Wade

This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

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Page Count

266

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475781377

ISBN 13

9781475781373

Selfsimilar Processes

By: Paul Embrechts

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Selfsimilar Processes

By: Paul Embrechts

The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

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Page Count

125

Publisher

Princeton University Press

Published Date

ISBN 10

1400825105

ISBN 13

9781400825103

Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

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Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

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374

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642146597

ISBN 13

9783642146596

Exercises and Solutions Manual for Integration and Probability

By Paul Malliavin

By: Paul Malliavin,Gerard Letac

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Exercises and Solutions Manual for Integration and Probability

By Paul Malliavin

By: Paul Malliavin,Gerard Letac

This book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.

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