In recent years products based on financial 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 financial 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 specific needs of particular investors and companies. The ability to handle efficiently and exploit successfully the opportunities arising from modern quantitative methods is now a key factor that differentiates market participants in both the finance and insurance fields. For these reasons it is important that financial institutions, insurance companies and corporations develop expertise in the area of quantitative finance, where many of the as- ciated quantitative methods and technologies emerge. This book aims to provide an introduction to quantitative finance. More precisely, it presents an introduction to the mathematical framework typically usedinfinancialmodeling,derivativepricing,portfolioselectionandriskm- agement. It offers a unified approach to risk and performance management by using the benchmark approach, which is different 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.