In recent years products based on financial derivatives have become an indis-
pensable tool for risk managers and investors. Insurance products have become
part of almost every personal and business portfolio. The management of mu-
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 tai-
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 asso-
ciated quantitative methods and technologies emerge.
This book aims to provide anintroduction to quantitative finance . More
precisely, it presents an introduction to the mathematical framework typically
used in financial modeling, derivative pricing, portfolio selection and risk man-
agement. It offers a unified approach to risk and performance management by
using thebenchmark approach , which is different to the prevailing paradigm
and will be described in a systematic and rigorous manner.
This approach uses thegrowth optimal portfolio as numeraire and the real
world probability measure as pricing measure. The existence of an equivalent
risk neutral probability measure is not required, which is one of the aspects
distinguishing the approach in this book from other more conventional texts
in the area. It is our experience that many practitioners find the use of the
real world probability measure attractive for pricingbecauseitisnaturaland
pricing can still be carried out even under circumstances when a risk neutral
probability measure cannot exist.
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