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Numerical Solution of Stochastic Differential Equations with Jumps in Finance

  • Eckhard Platen
  • Nicola Bruti-Liberati

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 64)

Table of contents

  1. Front Matter
    Pages I-XXVIII
  2. Eckhard Platen, Nicola Bruti-Liberati
    Pages 1-60
  3. Eckhard Platen, Nicola Bruti-Liberati
    Pages 61-137
  4. Eckhard Platen, Nicola Bruti-Liberati
    Pages 139-185
  5. Eckhard Platen, Nicola Bruti-Liberati
    Pages 187-231
  6. Eckhard Platen, Nicola Bruti-Liberati
    Pages 233-271
  7. Eckhard Platen, Nicola Bruti-Liberati
    Pages 273-307
  8. Eckhard Platen, Nicola Bruti-Liberati
    Pages 309-346
  9. Eckhard Platen, Nicola Bruti-Liberati
    Pages 347-388
  10. Eckhard Platen, Nicola Bruti-Liberati
    Pages 389-417
  11. Eckhard Platen, Nicola Bruti-Liberati
    Pages 419-475
  12. Eckhard Platen, Nicola Bruti-Liberati
    Pages 477-505
  13. Eckhard Platen, Nicola Bruti-Liberati
    Pages 507-522
  14. Eckhard Platen, Nicola Bruti-Liberati
    Pages 523-569
  15. Eckhard Platen, Nicola Bruti-Liberati
    Pages 571-590
  16. Eckhard Platen, Nicola Bruti-Liberati
    Pages 591-635
  17. Eckhard Platen, Nicola Bruti-Liberati
    Pages 637-695
  18. Eckhard Platen, Nicola Bruti-Liberati
    Pages 697-753
  19. Eckhard Platen, Nicola Bruti-Liberati
    Pages 755-780
  20. Back Matter
    Pages 781-856

About this book

Introduction

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Keywords

Variance jump diffusions linear optimization numerical methods quantitative finance simulation stochastic differential equations

Authors and affiliations

  • Eckhard Platen
    • 1
  • Nicola Bruti-Liberati
    • 2
  1. 1.Dept. Mathematical Sciences, School of Finance and Economics and DepaUniversity of Technology, SydneySydneyAustralia
  2. 2.Dept. Mathematical SciencesUniversity of Technology, SydneyBroadwayAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-13694-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12057-2
  • Online ISBN 978-3-642-13694-8
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site