This lecture series introduces a generalized framework for financial market modeling: the benchmark approach. It develops a unified treatment of derivative pricing, portfolio optimization, and risk management without assuming the existence of equivalent risk-neutral probability measures. The benchmark approach compatibly extends beyond the domain of classical asset pricing theories with significant implications for longer dated products, stochastic discount factors, and risk measures. A new Law of the Minimal Price, which generalizes the familiar Law of One Price, provides a revised foundation for derivative pricing. A Diversification Theorem justifies developing a simpler proxy for the full-blown numeraire portfolio.

The benchmark approach augments earlier financial modeling frameworks to enable tractable yet realistic market models encompassing equity indices, exchange rates, equities, and the interest rate term structure to be developed based solely upon the real world probability measure. The lecture series carefully explains how the benchmark approach differs from the classical risk-neutral approach. Examples will be presented, using long term and extreme maturity derivatives, to demonstrate the important fact that, in reality, a range of contracts can be less expensively priced and hedged than is suggested by classical theory.

The lecture series is based on the book co-authored by Eckhard Platen and David Heath, A Benchmark Approach to Quantitative Finance (Springer Finance, 2006, ISBN 3-540-26212-1). The core ideas from this book will be presented and further expanded upon during the seminar, including:

· Basing financial modeling on the key concept of a numeraire portfolio;

· Deriving the Law of the Minimal Price;

· Approximating the numeraire portfolio via diversification;

· Consistent utility maximization and portfolio optimization;

· Pricing nonreplicable claims consistently with replicable claims;

· Pricing and hedging long term and extreme maturity contracts;