Overview
- Authors:
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Eckhard Platen
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Dept. Mathematical Sciences, School of Finance and Economics and Depa, University of Technology, Sydney, Sydney, Australia
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Nicola Bruti-Liberati
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Dept. Mathematical Sciences, University of Technology, Sydney, Broadway, Australia
- 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
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Table of contents (18 chapters)
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Front Matter
Pages I-XXVIII
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 1-60
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 61-137
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 139-185
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 187-231
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 233-271
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 273-307
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 309-346
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 347-388
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 389-417
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 419-475
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 477-505
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 507-522
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 523-569
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 571-590
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 591-635
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 637-695
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 697-753
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- Eckhard Platen, Nicola Bruti-Liberati
Pages 755-780
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Back Matter
Pages 781-856
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
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Dept. Mathematical Sciences, School of Finance and Economics and Depa, University of Technology, Sydney, Sydney, Australia
Eckhard Platen
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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