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.

Finance
Financial Modeling
Hedging
Quantitative Methods
Statistical Methods
Stochastic Differential Equations
Stochastic Processes
Stochastic calculus
modeling
optimization
quantitative finance

Front Matter
Pages I-XX

Preliminaries from Probability Theory
Eckhard Platen, David Heath
Pages 1-53

Statistical Methods
Eckhard Platen, David Heath
Pages 55-98

Modeling via Stochastic Processes
Eckhard Platen, David Heath
Pages 99-132

Diffusion Processes
Eckhard Platen, David Heath
Pages 133-162

Martingales and Stochastic Integrals
Eckhard Platen, David Heath
Pages 163-203

The Itô Formula
Eckhard Platen, David Heath
Pages 205-235

Stochastic Differential Equations
Eckhard Platen, David Heath
Pages 237-275

Introduction to Option Pricing
Eckhard Platen, David Heath
Pages 277-318

Various Approaches to Asset Pricing
Eckhard Platen, David Heath
Pages 319-365

Continuous Financial Markets
Eckhard Platen, David Heath
Pages 367-402

Portfolio Optimization
Eckhard Platen, David Heath
Pages 403-437

Modeling Stochastic Volatility
Eckhard Platen, David Heath
Pages 439-481

Minimal Market Model
Eckhard Platen, David Heath
Pages 483-511

Markets with Event Risk
Eckhard Platen, David Heath
Pages 513-549

Numerical Methods
Eckhard Platen, David Heath
Pages 551-613

Solutions for Exercises
Eckhard Platen, David Heath
Pages 615-665

Back Matter
Pages 667-698

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.  Since this time his main research interests have focussed on the application of advanced numerical methods for the pricing and hedging of index, equity, FX and interest rate derivatives.  These numerical methods include PDE, Monte Carlo and Markov chain methods.  He has developed a range of new quantitative methods that are specifically designed for the benchmark approach. Dr Heath has authored more than thirteen publications in financial mathematics.

Book Title
A Benchmark Approach to Quantitative Finance

Authors
Eckhard Platen, David Heath

DOI
https://doi.org/10.1007/978-3-540-47856-0

eBook Packages
Mathematics and Statistics, Mathematics and Statistics (R0)

Hardcover ISBN
978-3-540-26212-1
Published: 26 September 2006

Softcover ISBN
978-3-642-06565-1
Published: 12 February 2010

eBook ISBN
978-3-540-47856-0
Published: 28 October 2006

Series ISSN
1616-0533

Series E-ISSN
2195-0687

Edition Number
1

Number of Pages
XVI, 700

Number of Illustrations
199 b/w illustrations

Topics
Public Economics, Quantitative Finance, Probability Theory and Stochastic Processes, Statistics for Business, Management, Economics, Finance, Insurance