Numerical Solution of Stochastic Differential Equations

The book presents many new results on higher-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential resarch problems in a field that is just beginning to expand rapidly and is widely applicable.

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. To help the reader develop an intuitive understanding and hands-on numerical skills, numerous exercises and PC-Exercises are included. The book is directed at a multi-disciplinary readership, consisting primarily of engineers, financial analysts, physicists and mathematicians developing numerical schemes for applications of SDEs, and also of researchers in other fields like biology, chemistry or economics who, with less mathematical background, wish to apply

The book is interdisciplinary in its appoach and orientation It places equal emphasis on both theory and applications Besides serving as a basic text on stochastic differential equations it derives and discusses the numerical methods needed to solve such equations Includes supplementary material: sn.pub/extras

Auteur
Professor Eckhard Platen is a joint appointment between the School of Finance and Economics and the Department of Mathematical Sciences to the 1997 created Chair in Quantitative Finance at the University of Technology Sydney. Prior to this appointment he was Founding Head of the Centre for Financial Mathematics at the Institute of Advanced Studies at the Australian National University in Canberra. He completed a PhD in Mathematics at the Technical University in Dresden in 1975 and obtained in 1985 his Dr. sc. from the Academy of Sciences in Berlin, where he headed at the Weierstrass Institute the Sector of Stochastics. He is co-author of two successful books on Numerical Methods for Stochastic Differential Equations, published by Springer Verlag, and has authored more than 100 research papers in quantitative finance and mathematics.

Résumé
"... the authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible. This was not an easy task... Their exposition stresses clarity, not formality - a very welcome approach." ZAMP

Contenu

1. Probability and Statistics.- 2. Probability and Stochastic Processes.- 3. Ito Stochastic Calculus.- 4. Stochastic Differential Equations.- 5. Stochastic Taylor Expansions.- 6. Modelling with Stochastic Differential Equations.- 7. Applications of Stochastic Differential Equations.- 8. Time Discrete Approximation of Deterministic Differential Equations.- 9. Introduction to Stochastic Time Discrete Approximation.- 10. Strong Taylor Approximations.- 11. Explicit Strong Approximations.- 12. Implicit Strong Approximations.- 13. Selected Applications of Strong Approximations.- 14. Weak Taylor Approximations.- 15. Explicit and Implicit Weak Approximations.- 16. Variance Reduction Methods.- 17. Selected Applications of Weak Approximations.- Solutions of Exercises.- Bibliographical Notes.