Numerical solution of stochastic differential equations with jumps in finance

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 morecomplex 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. The presented bookis accessible to a wide readership and contains many new results on numericalmethods 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. INDICE: Preface.- Suggestions for the Reader.- Basic Notation.- Motivationand Brief Survey.- 1. SDEs with Jumps.- 2. Exact Simulation of Solutions of SDEs.- 3. Benchmark Approach to Finance.- 4. Stochastic Expansions.- 5. Introduction to Scenario Simulation.- 6. Regular Strong Taylor Approximations.- 7. Regular Strong Itô Approximations.- 8. Jump-Adapted Strong Approximations.- 9. Estimating Discretely Observed Diffusions.- 10. Filtering.- 11. Monte Carlo Simulation of SDEs.- 12. Regular Weak Taylor Approximations.- 3. Jump-Adapted Weak Approximations.- 14. Numerical Stability.- 15. Martingale Representations and Hedge Ratios.- 16. Variance Reduction Techniques.- 17. Trees and Markov Chain Approximations.- 18. Solutions for Exercises.- Acknowledgements.- Bibliographical Notes.- References.- Author Index.- Index.

• ISBN: 978-3-642-12057-2
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 856
• Fecha Publicación: 01/08/2010
• Nº Volúmenes: 1
• Idioma: Inglés