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...

Is it possible to achieve almost riskless investment results in the long run through equity investments? The persistence of low interest rates is spurring research on this question, because of the need to increase yields, while limiting variability of investment results. Target date funds aim to...

A major problem in financial engineering is investing on financial markets for long horizons. At infinite horizons, dynamic versions of the Kelly strategy are mathematically certain to maximize growth, such that these growth-optimal portfolios outperform all other investment strategies. This...

In the years following the publication of Black and Scholes [7], numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump diffusion models, and models based on Levy processes. These all have their own...

This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic volatility model that recovers not only the typically observed implied volatility smiles and skews for short dated vanilla foreign exchange options but allows one also to price payoffs...

Recursive marginal quantization (RMQ) allows the construction of optimal discrete grids for approximating solutions to stochastic differential equations in d-dimensions. Product Markovian quantization (PMQ) reduces this problem to d one-dimensional quantization problems by recursively...

This paper introduces a more general modeling world than available under the classical no-arbitrage paradigm in finance. New research questions and interesting related econometric studies emerge naturally. To explain in this paper the new approach and illustrate first important consequences, we...

In an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable magnitude at predictable times. We provide a rigorous formulation of this result in a fully general setting, without imposing any semimartingale restriction and only allowing for...

In this paper, we present an alternative approach as a suitable framework under which liability driven investments can be valued and hedged. This benchmark approach values both assets and liabilities consistently under the real world probability measure using the best performing portfolio, the...

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....