This paper introduces a benchmark model for financial markets, which is based on the unique characterization of a benchmark portfolio that is chosen to be the growth optimal portfolio. The general structure of risk premia for asset prices and portfolios is derived. Furthermore, the short rate is...

Monetary policy has pursued the concept of inflation targeting. This has been implemented in many countries. Here interest rates are supposed to respond to an inflation gap and output gap. Yet, recently monetary policy, in particular in the US after the subprime and the credit crises, the...

This paper describes a financial market modelling framework that exploits the notion of a deflator . The denominations of the deflator measured in units of primary assets form a minimal set of basic financial quantities that completely specify the overall market dynamics, where deflated asset...

The paper proposes a financial market model that generates stochastic volatility and stochastic interest rate using a minimal number of factors that characterise the dynamics of the different denominations of the deflator. It models asset prices essentially as functionals of square root and...

The paper derives a parsimonious model for the long-term dynamics of a well-diversified stock index, the S&P500. The index is modeled as growth optimal portfolio. Its normalized value evolves, in some market time, as a square root process. The derivative of market time is a linear function of...

This paper aims to unify and generalize several of the widely-used pricing approaches for long-dated contracts with a focus on market-consistent valuation. It proposes a loading pricing concept that combines the theoretically possible minimal price of a contract with its formally obtained risk...

The need for the management of risks related to the COVID-19 epidemic in health, economics, finance and insurance became obvious after its outbreak. As a basis for respective quantitative methods, the paper models in a novel manner the dynamics of an epidemic via a four-dimensional stochastic...

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the...

This paper introduces a general market modeling framework, the benchmark approach, which assumes the existence of the numeraire portfolio. This is the strictly positive portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales, that is intuitively...

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numerraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Follmer, Sondermann and Schweizer....