Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Springer Science & Business Media
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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.
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About the author

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
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Additional Information

Publisher
Springer Science & Business Media
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Published on
Jul 23, 2010
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Pages
856
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ISBN
9783642136948
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Best For
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Language
English
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Genres
Business & Economics / Accounting / General
Business & Economics / Statistics
Mathematics / Applied
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
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Content Protection
This content is DRM protected.
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Eckhard Platen
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For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.

And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

Peter Eris Kloeden
The numerical solution of stochastic differential equations is becoming an in dispensible worktool in a multitude of disciplines, bridging a long-standing gap between the well advanced theory of stochastic differential equations and its application to specific examples. This has been made possible by the much greater accessibility to high-powered computers at low-cost combined with the availability of new, effective higher order numerical schemes for stochastic dif ferential equations. Many hitherto intractable problems can now be tackled successfully and more realistic modelling with stochastic differential equations undertaken. The aim of this book is to provide a computationally oriented introduction to the numerical solution of stochastic differential equations, using computer experiments to develop in the readers an ability to undertake numerical studies of stochastic differential equations that arise in their own disciplines and an understanding, intuitive at least, of the necessary theoretical background. It is related to, but can also be used independently of the monograph P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Applications of Mathematics Series Vol. 23, Springer-Verlag, Hei delberg, 1992, which is more theoretical, presenting a systematic treatment of time-discretized numerical schemes for stochastic differential equations along with background material on probability and stochastic calculus. To facilitate the parallel use of both books, the presentation of material in this book follows that in the monograph closely.
Eckhard Platen
In recent years products based on ?nancial derivatives have become an ind- pensabletoolforriskmanagersandinvestors. Insuranceproductshavebecome part of almost every personal and business portfolio. The management of - tual and pension funds has gained in importance for most individuals. Banks, insurance companies and other corporations are increasingly using ?nancial and insurance instruments for the active management of risk. An increasing range of securities allows risks to be hedged in a way that can be closely t- lored to the speci?c needs of particular investors and companies. The ability to handle e?ciently and exploit successfully the opportunities arising from modern quantitative methods is now a key factor that di?erentiates market participants in both the ?nance and insurance ?elds. For these reasons it is important that ?nancial institutions, insurance companies and corporations develop expertise in the area of quantitative ?nance, where many of the as- ciated quantitative methods and technologies emerge. This book aims to provide an introduction to quantitative ?nance. More precisely, it presents an introduction to the mathematical framework typically usedin?nancialmodeling,derivativepricing,portfolioselectionandriskm- agement. It o?ers a uni?ed approach to risk and performance management by using the benchmark approach, which is di?erent to the prevailing paradigm and will be described in a systematic and rigorous manner. This approach uses the growth optimal portfolio as numeraire and the real world probability measure as pricing measure.
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