Numerical Solution of Stochastic Differential Equations with Jumps in Finance

• Main Authors: Platen, Eckhard. (Author), Bruti-Liberati, Nicola. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Stochastic Modelling and Applied Probability, 64
• Subjects: Mathematics.; Finance.; Distribution (Probability theory).; Economics > Statistics.; Probability Theory and Stochastic Processes.; Statistics for Business/Economics/Mathematical Finance/Insurance.; Quantitative Finance.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-13694-8

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, descri...

Table of Contents:

• Preface
• Suggestions for the Reader
• Basic Notation
• Motivation and 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 It ̥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.