A benchmark approach to quantitative finance

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.