Numerical Solution of SDE Through Computer Experiments

Author: Peter Eris Kloeden
Publisher: Springer Science & Business Media
ISBN: 3642579132
Format: PDF, Docs
Download Now
This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations. It also creates an intuitive understanding of the necessary theoretical background. Software containing programs for over 100 problems is available online.

Numerical Solution of Stochastic Differential Equations

Author: Peter E. Kloeden
Publisher: Springer Science & Business Media
ISBN: 3662126168
Format: PDF, Kindle
Download Now
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "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." --ZAMP

Tools for Computational Finance

Author: Rüdiger U. Seydel
Publisher: Springer
ISBN: 1447173384
Format: PDF, Kindle
Download Now
Computational and numerical methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to anyone working in computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its sixth edition, Tools for Computational Finance has been significantly revised and contains: Several new parts such as a section on extended applications of tree methods, including multidimensional trees, trinomial trees, and the handling of dividends; Additional material in the field of generating normal variates with acceptance-rejection methods, and on Monte Carlo methods; 115 exercises, and more than 100 figures, many in color. Written from the perspective of an applied mathematician, all methods are introduced for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book, enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate and graduate students in mathematics, engineering, and other scientific disciplines as well as professionals in financial engineering.

Numerical Solution of Stochastic Differential Equations

Author: Peter E. Kloeden
Publisher: Springer Science & Business Media
ISBN: 3662126168
Format: PDF
Download Now
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "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." --ZAMP

Theory and Numerics of Differential Equations

Author: James Blowey
Publisher: Springer Science & Business Media
ISBN: 3662043548
Format: PDF, Mobi
Download Now
A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 364213694X
Format: PDF, Mobi
Download Now
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.

Robust Statistics Data Analysis and Computer Intensive Methods

Author: Helmut Rieder
Publisher: Springer Science & Business Media
ISBN: 1461223806
Format: PDF, Mobi
Download Now
To celebrate Peter Huber's 60th birthday in 1994, our university had invited for a festive occasion in the afternoon of Thursday, June 9. The invitation to honour this outstanding personality was followed by about fifty colleagues and former students from, mainly, allover the world. Others, who could not attend, sent their congratulations by mail and e-mail (P. Bickel:" ... It's hard to imagine that Peter turned 60 ... "). After a welcome address by Adalbert Kerber (dean), the following lectures were delivered. Volker Strassen (Konstanz): Almost Sure Primes and Cryptography -an Introduction Frank Hampel (Zurich): On the Philosophical Foundations of Statistics 1 Andreas Buja (Murray Hill): Projections and Sections High-Dimensional Graphics for Data Analysis. The distinguished speakers lauded Peter Huber a hard and fair mathematician, a cooperative and stimulating colleague, and an inspiring and helpful teacher. The Festkolloquium was surrounded with a musical program by the Univer 2 sity's Brass Ensemble. The subsequent Workshop "Robust Statistics, Data Analysis and Computer Intensive Methods" in Schloss Thurnau, Friday until Sunday, June 9-12, was organized about the areas in statistics that Peter Huber himself has markedly shaped. In the time since the conference, most of the contributions could be edited for this volume-a late birthday present-that may give a new impetus to further research in these fields.

Brownian Motion Calculus

Author: Ubbo F. Wiersema
Publisher: John Wiley & Sons
ISBN: 0470021713
Format: PDF
Download Now
Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.

Mathematical Modeling for the Life Sciences

Author: Jacques Istas
Publisher: Springer Science & Business Media
ISBN: 354027877X
Format: PDF, Docs
Download Now
Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading