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A Benchmark Approach to Quantitative Finance

Eckhard Platen, David Heath (Autoren)

Buch | Hardcover

XVI, 700 Seiten

2006 | 2006
Springer Berlin (Verlag)
978-3-540-26212-1 (ISBN)

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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.

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.

Dr David Heath works as a Senior Research Fellow in Quantitative Finance at the University of Technology, Sydney. During the early 1990s he became interested in various aspects of quantitative finance. He completed his PhD in financial mathematics at the Australian National University at the Centre for Financial Mathematics in 1995.

Preliminaries from Probability Theory.- Statistical Methods.- Modeling via Stochastic Processes.- Diffusion Processes.- Martingales and Stochastic Integrals.- The Itô Formula.- Stochastic Differential Equations.- to Option Pricing.- Various Approaches to Asset Pricing.- Continuous Financial Markets.- Portfolio Optimization.- Modeling Stochastic Volatility.- Minimal Market Model.- Markets with Event Risk.- Numerical Methods.- Solutions for Exercises.

lt;p>From the reviews:

"The book under review introduces quantitative finance using the benchmark approach. ... It is quite a nice blend of narrative and mathematics. There are also some bigger examples which contribute nicely to the overall presentation. ... Exercises are provided at the end of each chapter. The authors even provide solutions to exercises. ... I think it could be quite useful for students, because of the first part of the book, and to practitioners, due to the exposition in the second part of the book." (Ita Cirovic Donev, MathDL, March, 2007)

"This book provides an introduction to quantitative finance. ... It aims to stimulate interest in the benchmark approach by describing some of its power and wide applicability. It is intended for quantitative analysts postgraduate students, practioners in finance, economics and insurance. ... It is designed for three groups of users. Firstly, it provides useful information to financial analysts and practioners. Secondly, it aims to introduce those with a reasonable basic mathematical background. Thirdly, researchers may find the later parts of the book interesting ... ." (Klaus Ehemann, Zentralblatt MATH, Vol. 1104 (6), 2007)

"The book is a rather comprehensive treatment of quantitative finance and distinguishes itself from other analogous treatments by using a novel approach that allows one to generalize various existing results and to some extent also allows one to bridge a certain gap between current and classical approaches. ... The comprehensiveness of the book is very valuable for research ... ." (Wolfgang J. Runggaldier, Mathematical Reviews, Issue 2008 d)

"A comprehensive introduction to the mathematical foundations of finance. It is thorough and encyclopedic, providing a wide range of definitions and theorems that are useful in the subject. ... a valuable text for well-motivated students interested in these topics, whether they are pursuing problems within the classical framework or beyond the assumptions of the basic theory." (Gunduz Caginalp, SIAM Review, Vol. 52 (2), 2010)

Erscheint lt. Verlag	26.9.2006
Reihe/Serie	Springer Finance
Zusatzinfo	XVI, 700 p. 199 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1336 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Volkswirtschaftslehre ► Wirtschaftspolitik
Schlagworte	Benchmark approach • Finance • Financial market modeling • financial modeling • Finanzmarkt • Hedging • mathematical finance • Minimal market model • Modeling • MSC (2000): 90A12, 60G30, 62P20 • ökonomische Modelle • Optimization • Quantitative Finance • Quantitative Methods • Statistical Methods • Stochastic Calculus • Stochastic differential equations • Stochastic Processes • Stochastik
ISBN-10	3-540-26212-1 / 3540262121
ISBN-13	978-3-540-26212-1 / 9783540262121
Zustand	Neuware