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Lévy Matters I

Recent Progress in Theory and Applications: Foundations, Trees and Numerical Issues in Finance

  • Book
  • © 2010

Overview

Authors:
  1. Thomas Duquesne

    1. Lab de Probabilités & Modèles Aléatoires, Univ Paris 6 - Pierre et Marie Curie, Paris Cedex 05, France

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  2. Oleg Reichmann

    1. Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

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  3. Ken-iti Sato

    1. Tenpaku-Ku, Nagoya, Japan

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  4. Christoph Schwab

    1. Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

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Editors:
  1. Ole E Barndorff-Nielsen

    1. Thiele Centre, Department of Mathematics, Aarhus University, Aarhus C, Denmark

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  2. Jean Bertoin

    1. , Lab de Probabilités & Modèles Aléatoires, Univ Paris 6 - Pierre et Marie Curie, Paris Cedex 05, France

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  3. Jean Jacod

    1. Pierre et Marie Curie, Institut de Mathématiques de Jussieu, Université Paris VI -, Paris, Cedex 05, France

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  4. Claudia Klüppelberg

    1. Center for Mathematical Sciences, Munich University of Technology, Garching, Germany

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  • Over the past 10-15 years, we have seen a revival of general Lévy processes theory as well as a burst of new applications
  • There is a lively and growing research community in this area
  • Expository articles help to disseminate important theoretical and applied research to other researchers and in particular to young researchers like PhD students and Postdocs
  • Chapters attract different focus groups of readers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2001)

Part of the book sub series: Lévy Matters (LEVY)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Fractional Integrals and Extensions of Selfdecomposability

    • Ken-iti Sato
    Pages 1-91

  3. Packing and Hausdorff Measures of Stable Trees

    • Thomas Duquesne
    Pages 93-136

  4. Numerical Analysis of Additive, Lévy and Feller Processes with Applications to Option Pricing

    • Oleg Reichmann, Christoph Schwab
    Pages 137-196

  5. Back Matter

    Pages 197-204
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Keywords

About this book

This is the first volume of a subseries of the Lecture Notes in Mathematics which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Lévy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The three expository articles of this first volume have been chosen to reflect the breadth of the area of Lévy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on R^d. The second article by Thomas Duquesne discusses Hausdorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Lévy or additive processes model the dynamics of the risky assets.

Authors, Editors and Affiliations

  • Thiele Centre, Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Ole E Barndorff-Nielsen

  • , Lab de Probabilités & Modèles Aléatoires, Univ Paris 6 - Pierre et Marie Curie, Paris Cedex 05, France

    Jean Bertoin

  • Pierre et Marie Curie, Institut de Mathématiques de Jussieu, Université Paris VI -, Paris, Cedex 05, France

    Jean Jacod

  • Center for Mathematical Sciences, Munich University of Technology, Garching, Germany

    Claudia Klüppelberg

  • Lab de Probabilités & Modèles Aléatoires, Univ Paris 6 - Pierre et Marie Curie, Paris Cedex 05, France

    Thomas Duquesne

  • Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

    Oleg Reichmann, Christoph Schwab

  • Tenpaku-Ku, Nagoya, Japan

    Ken-iti Sato

Bibliographic Information

  • Book Title: Lévy Matters I

  • Book Subtitle: Recent Progress in Theory and Applications: Foundations, Trees and Numerical Issues in Finance

  • Authors: Thomas Duquesne, Oleg Reichmann, Ken-iti Sato, Christoph Schwab

  • Editors: Ole E Barndorff-Nielsen, Jean Bertoin, Jean Jacod, Claudia Klüppelberg

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-14007-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Softcover ISBN: 978-3-642-14006-8Published: 05 September 2010

  • eBook ISBN: 978-3-642-14007-5Published: 02 September 2010

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 206

  • Topics: Probability Theory and Stochastic Processes

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