The investment industry lacks an unified framework for handling derivative instruments in general portfolio management. With the increased use of derivatives, there is a need for a framework that aligns fundamental terminology and concepts. The main challenges with the current practices are...

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of...

In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

An investor faced with a contingent claim may eliminate risk by (super-)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

This paper is the first to analyze and value early exercises of Individual Investors in fixed-income investment products. Assuming decision and transaction costs we consider that a continuous decision-making on holding or exercising is not optimal anymore and propose a new approach to modeling...

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...

In this paper we introduce a discrete time pricing model for a European call option when the log-return of the underlying stock (asset) is subject to discontinuous market regime type of shifts in its mean or volatility whose risk can be priced in the market. The paper shows how to estimate this...

We investigate the effect of including variance derivatives as calibration and hedging instruments for pricing and hedging exotic structures. This is studied empirically using market data for SPX and VIX derivatives applied in a stochastic volatility jump diffusion model