This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...

This paper approximates stochastic integrals with respect to the geometric Brownian motion by stochastic integrals over discretized integrands, where deterministic, but not necessarily equidistant, time nets are used.

In the research project "MetPVNet", both, the forecast-based operation management in distribution grids and as well as the forecasts of the feed-in of PV-power from decentralized plants could be improved on the basis of satellite data and numerical weather forecasts. Based on a detailed network...

In the research project "MetPVNet", both, the forecast-based operation management in distribution grids and as well as the forecasts of the feed-in of PV-power from decentralized plants could be improved on the basis of satellite data and numerical weather forecasts. Based on a detailed network...

We study the problem of estimating the coefficients of a diffusion (Xl, t 2: 0); the estimation is based on discrete data Xn . . n = 0, 1, ... ,N. The sampling frequency delta t is constant , and asymptotics arc taken at the number of observations tends to infinity. We prove that the problem of...

In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by...

Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an...