Numerical Solution of Stochastic Differential Equations with Jumps in Finance
Authors: Platen, Eckhard, Bruti-Liberati, Nicola
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- Contains many new results on numerical methods but also innovative methodologies in quantitative finance
- Exercises with solutions are included to help the reader to develop a good understanding of the underlying mathematics
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- About this Textbook
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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.
- About the authors
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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
- Table of contents (18 chapters)
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Stochastic Differential Equations with Jumps
Pages 1-60
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Exact Simulation of Solutions of SDEs
Pages 61-137
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Benchmark Approach to Finance and Insurance
Pages 139-185
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Stochastic Expansions
Pages 187-231
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Introduction to Scenario Simulation
Pages 233-271
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Table of contents (18 chapters)
- Download Preface 1 PDF (99.6 KB)
- Download Sample pages 2 PDF (1.6 MB)
- Download Table of contents PDF (103.1 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Numerical Solution of Stochastic Differential Equations with Jumps in Finance
- Authors
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- Eckhard Platen
- Nicola Bruti-Liberati
- Series Title
- Stochastic Modelling and Applied Probability
- Series Volume
- 64
- Copyright
- 2010
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-13694-8
- DOI
- 10.1007/978-3-642-13694-8
- Hardcover ISBN
- 978-3-642-12057-2
- Softcover ISBN
- 978-3-662-51973-8
- Series ISSN
- 0172-4568
- Edition Number
- 1
- Number of Pages
- XXVIII, 856
- Topics
