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Functionals of Multidimensional Diffusions with Applications to Finance

  • Book
  • © 2013

Overview

Authors:
  1. Jan Baldeaux

    1. University of Technology Sydney Finance Discipline Group, Haymarket, Australia

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    You can also search for this author in PubMed   Google Scholar

  2. Eckhard Platen

    1. University of Technology Sydney Finance Discipline Group, Haymarket, Australia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides the reader in a systematic way with the ability to derive explicit formulas for functionals of multidimensional diffusions
  • Special unique chapters on Lie symmetry group methods and matrix valued Wishart processes
  • Provides the most recent introduction to the benchmark approach to finance pioneered by Platen and co-authors
  • The reader finds readily applicable exact simulation methods for various multidimensional diffusion processes?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Bocconi & Springer Series (BS, volume 5)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XXIII
    Download chapter PDF

  2. A Benchmark Approach to Risk Management

    • Jan Baldeaux, Eckhard Platen
    Pages 1-21

  3. Functionals of Wiener Processes

    • Jan Baldeaux, Eckhard Platen
    Pages 23-63

  4. Functionals of Squared Bessel Processes

    • Jan Baldeaux, Eckhard Platen
    Pages 65-99

  5. Lie Symmetry Group Methods

    • Jan Baldeaux, Eckhard Platen
    Pages 101-140

  6. Transition Densities via Lie Symmetry Methods

    • Jan Baldeaux, Eckhard Platen
    Pages 141-159

  7. Exact and Almost Exact Simulation

    • Jan Baldeaux, Eckhard Platen
    Pages 161-180

  8. Affine Diffusion Processes on the Euclidean Space

    • Jan Baldeaux, Eckhard Platen
    Pages 181-198

  9. Pricing Using Affine Diffusions

    • Jan Baldeaux, Eckhard Platen
    Pages 199-217

  10. Solvable Affine Processes on the Euclidean State Space

    • Jan Baldeaux, Eckhard Platen
    Pages 219-241

  11. An Introduction to Matrix Variate Stochastics

    • Jan Baldeaux, Eckhard Platen
    Pages 243-259

  12. Wishart Processes

    • Jan Baldeaux, Eckhard Platen
    Pages 261-297

  13. Monte Carlo and Quasi-Monte Carlo Methods

    • Jan Baldeaux, Eckhard Platen
    Pages 299-322

  14. Computational Tools

    • Jan Baldeaux, Eckhard Platen
    Pages 323-341

  15. Credit Risk Under the Benchmark Approach

    • Jan Baldeaux, Eckhard Platen
    Pages 343-362

  16. Continuous Stochastic Processes

    • Jan Baldeaux, Eckhard Platen
    Pages 363-387

  17. Time-Homogeneous Scalar Diffusions

    • Jan Baldeaux, Eckhard Platen
    Pages 389-395

  18. Detecting Strict Local Martingales

    • Jan Baldeaux, Eckhard Platen
    Pages 397-403

  19. Back Matter

    Pages 405-425
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Keywords

About this book

This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Reviews

“The textbook at hand focuses on ‘tractable multidimensional models with functionals that have explicit solutions’. … The book also covers in detail numerical techniques such exact and almost exact simulation, transform methods, and quasi-Monte Carlo schemes. Moreover, it contains a self-contained summary of the tools from stochastic calculus that are used in the main body of the text.” (Johannes Muhle-Karbe, zbMATH 1401.60001, 2019)


From the book reviews:

“This book is a valuable contribution to the literature on applications of stochastic processes to financial mathematics, and can serve as a useful introduction to the various techniques needed in order to derive closed form expressions for a variety of functionals of multidimensional diffusions arising in financial models but also as a useful reference book, in which researchers and practitioners may retrieve various useful results.” (Athanasios Yannacopoulos, Mathematical Reviews, March, 2015)

Authors and Affiliations

  • University of Technology Sydney Finance Discipline Group, Haymarket, Australia

    Jan Baldeaux, Eckhard Platen

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