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Numerical Solution of Stochastic Differential Equations with Jumps in Finance

  • Textbook
  • © 2010

Overview

Authors:
  1. Eckhard Platen

    1. Dept. Mathematical Sciences, School of Finance and Economics and Depa, University of Technology, Sydney, Sydney, Australia

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    You can also search for this author in PubMed   Google Scholar

  2. Nicola Bruti-Liberati

    1. Dept. Mathematical Sciences, University of Technology, Sydney, Broadway, Australia

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    You can also search for this author in PubMed   Google Scholar

  • The presented book is accessible to a wide readership and contains many new results on numerical methods but also innovative methodologies in quantitative finance.
  • To help the reader to develop a good understanding of the underlying mathematics, exercises with solutions are included.
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XXVIII
    Download chapter PDF

  2. Stochastic Differential Equations with Jumps

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 1-60

  3. Exact Simulation of Solutions of SDEs

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 61-137

  4. Benchmark Approach to Finance and Insurance

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 139-185

  5. Stochastic Expansions

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 187-231

  6. Introduction to Scenario Simulation

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 233-271

  7. Regular Strong Taylor Approximations with Jumps

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 273-307

  8. Regular Strong Itô Approximations

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 309-346

  9. Jump-Adapted Strong Approximations

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 347-388

  10. Estimating Discretely Observed Diffusions

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 389-417

  11. Filtering

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 419-475

  12. Monte Carlo Simulation of SDEs

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 477-505

  13. Regular Weak Taylor Approximations

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 507-522

  14. Jump-Adapted Weak Approximations

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 523-569

  15. Numerical Stability

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 571-590

  16. Martingale Representations and Hedge Ratios

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 591-635

  17. Variance Reduction Techniques

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 637-695

  18. Trees and Markov Chain Approximations

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 697-753

  19. Solutions for Exercises

    • Eckhard Platen, Nicola Bruti-Liberati
    Pages 755-780

  20. Back Matter

    Pages 781-856
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Keywords

About this book

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 quantitativemethods, 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.

Authors and Affiliations

  • Dept. Mathematical Sciences, School of Finance and Economics and Depa, University of Technology, Sydney, Sydney, Australia

    Eckhard Platen

  • Dept. Mathematical Sciences, University of Technology, Sydney, Broadway, Australia

    Nicola Bruti-Liberati

About the authors

Prof. Eckhard Platen holds the Chair in Quantitative Finance at the University of Technology, Sydney. Author of books on numerical methods for stochastic differential equations and recent book on benchmark approach at Springer Verlag. Has written more than 140 papers in finance, insurance and applied mathematics and serves on the editorial boards of five international journals including Mathematical Finance and Quantitative Finance

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