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...

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...

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...

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...

This paper considers a new class of Monte Carlo methods that are combined with PDE expansions for the pricing and hedging of derivative securities for multidimensional diffusion models. The proposed method combines the advantages of both PDE and Monte Carlo methods and can be directly applied to...

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a...

Estimation theory has shown, due to the limited estimation window available for real asset data, the sample based Markowitz mean-variance approach produces unreliable weights which fluctuate substantially over time. This paper proposes an alternate approach to portfolio optimization, being 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...

This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling and risk measurement. It is based on the natural assumption that investors prefer more or less, in the sense that the higher drift is preferred. Each such investor is shown to hold an...

This paper proposes a consistent benchmark approach to price weather derivatives. The growth optimal portfolio to price weather derivatives. The growth optimal portfolio is used as numeraire such that all benchmarked fair price processes are martingales. No measure transformation is needed for...