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© 2013

Functionals of Multidimensional Diffusions with Applications to Finance

Book

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

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Jan Baldeaux, Eckhard Platen
    Pages 1-21
  3. Jan Baldeaux, Eckhard Platen
    Pages 23-63
  4. Jan Baldeaux, Eckhard Platen
    Pages 65-99
  5. Jan Baldeaux, Eckhard Platen
    Pages 101-140
  6. Jan Baldeaux, Eckhard Platen
    Pages 141-159
  7. Jan Baldeaux, Eckhard Platen
    Pages 161-180
  8. Jan Baldeaux, Eckhard Platen
    Pages 181-198
  9. Jan Baldeaux, Eckhard Platen
    Pages 199-217
  10. Jan Baldeaux, Eckhard Platen
    Pages 219-241
  11. Jan Baldeaux, Eckhard Platen
    Pages 243-259
  12. Jan Baldeaux, Eckhard Platen
    Pages 261-297
  13. Jan Baldeaux, Eckhard Platen
    Pages 299-322
  14. Jan Baldeaux, Eckhard Platen
    Pages 323-341
  15. Jan Baldeaux, Eckhard Platen
    Pages 343-362
  16. Jan Baldeaux, Eckhard Platen
    Pages 363-387
  17. Jan Baldeaux, Eckhard Platen
    Pages 389-395
  18. Jan Baldeaux, Eckhard Platen
    Pages 397-403
  19. Back Matter
    Pages 405-425

About this book

Introduction

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.​

Keywords

benchmark approach derivative pricing diffusions functionals lie symmetry methods

Authors and affiliations

  1. 1.University of Technology Sydney Finance Discipline GroupHaymarketAustralia
  2. 2.University of Technology Sydney Finance Discipline GroupHaymarketAustralia

Bibliographic information

Industry Sectors
Finance, Business & Banking

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)