The purpose of this paper is to study the efficiency of simplified weak schemes for stochastic differential equations. We present a numerical comparison between weak Taylor schemes and their simplified versions. In the simplified schemes discrete random variables, instead of Gaussian ones, are...

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For...

Event-driven uncertainties such as corporate defaults, operational failures or central bank announcements are important elements in the modelling of financial quantities. Therefore, stochastic differential equations (SDEs) of jump-diffusion type are often used in finance. We consider in this...

This paper proposes analternative approach to the modeling of the interest rate term structure. It suggests that the total market price for risk is an important factor that has to be modeled carefully. The growth optimal portfolio, which is characterized by this factor, is used as refernce unit...

This paper introduces a realistic, generalized market modeling framework for which the Law of One Price no longer holds. Instead the Law of the Minimal Price will be derived, which for contingent claims with long term to maturity may provide significantly lower prices than suggested under the...

This paper constructs and compares various total return world stock indices based on daily data. Due to diversification these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio. The paper constructs a...

This paper proposes an approach to the intraday analysis of the dynamics of electricity prices. The Growth Optimal Portfolio (GOP) is used as a reference unit in a continuous financial electricity price model. A diversified global portfolio in the form of a market capitalisation weighted index...

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which...

The paper proposes the use of the growth optimal portfolio for the construction of financial market models with unobserved factors that have to be filtered. This benchmark approach avoids any measure transformation for the pricing of derivatives. The suggested framework allows to measure the...

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the...