rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Pricing Derivatives Under Lévy Models
    sub title: Modern Finite-Difference and Pseudo-Differential Operators Approach
  name:
    name part: Itkin, Andrey.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 308 p. 64 illus., 62 illus. in color. online resource.
  abstract: This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.
  table of contents: Basics of a finite-difference method -- Modern finite-difference approach -- An M-matrix theory and FD -- Brief Introduction into Lévy processes -- Pseudo-parabolic and fractional equations of option pricing -- Pseudo-parabolic equations for various Lévy models -- High-order splitting methods for forward PDEs and PIDEs -- Multi-dimensional structural default models and correlated jumps -- LSV models with stochastic interest rates and correlated jumps -- Stochastic skew model -- Glossary -- References -- Index.
  note: by Andrey Itkin.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Economics, Mathematical
  subject:
    topic: Computer mathematics
  subject:
    topic: Mathematical models
  subject:
    topic: Mathematics
  subject:
    topic: Quantitative Finance
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Computational Science and Engineering
  subject:
    topic: Partial Differential Equations
  classification: HB135-147
  classification: 519
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Pseudo-Differential Operators, Theory and Applications, 12
  identifier: 9781493967926
  identifier: http://dx.doi.org/10.1007/978-1-4939-6792-6
  record info:
    record creation date: 170227
    record change date: 20170227140902.0
    record identifier: 978-1-4939-6792-6