Self-dual continuous processes

The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self-dual processes. Moreover, we give a characterisation of continuous Ocone martingales via a strong version of self-duality

Exchangeability type properties of asset prices

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Levy processes. Based on this, concrete semi-static hedging techniques for multi-asset barrier options, such as certain weighted barrier spread options, weighted barrier swap options or weighted barrier quanto-swap options are suggested.Comment: The final version of the paper "Semi-static hedging under exchangeability type conditions". To appear in Advances in Applied Probabilit

Invariance properties of random vectors and stochastic processes based on the zonoid concept

Two integrable random vectors $\xi$ and $\xi^*$ in $\mathbb {R}^d$ are said to be zonoid equivalent if, for each $u\in \mathbb {R}^d$, the scalar products $\langle\xi,u\rangle$ and $\langle\xi^*,u\rangle$ have the same first absolute moments. The paper analyses stochastic processes whose finite-dimensional distributions are zonoid equivalent with respect to time shift (zonoid stationarity) and permutation of its components (swap invariance). While the first concept is weaker than the stationarity, the second one is a weakening of the exchangeability property. It is shown that nonetheless the ergodic theorem holds for swap-invariant sequences and the limits are characterised.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ519 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Turbulent exchange of carbon dioxide in a complex urban environment : results from Long-term Eddy Covariance measurements

Within this thesis, characteristics of the turbulent exchange within the urban boundary layer, as well as long-term trends and tendencies of the carbon dioxide flux (FC) and concentration (rhoC) are presented. Prevailing transport processes, the transfer and transport efficiencies of the turbulent exchange of momentum, heat, CO2 and H2O and the importance of coherent turbulent motions within the urban boundary layer are studied by applying the quadrant analysis technique. The behavior of FC and rhoC in the urban environment is investigated on daily, seasonal, and inter-annual scales as well as in comparison to regional background concentration records of the atmospheric CO2 concentration. The dependence of the passive scalars CO2 and H2O on atmospheric stability (zeta) differs distinctly in comparison to momentum and heat. The vertical fluxes of momentum (tau) and heat (QH) are actively generating mechanically and buoyantly driven turbulence, respectively. Due to the strong coupling between tau, QH and zeta, each stability class is characterized by a distinctive turbulence regime. In contrast, the turbulent exchange of CO2 and H2O is not primarily controlled by the existence of transporting eddies, but also heavily influenced by the activity and the composition of the corresponding scalar sources (e.g. traffic, heating etc.) and thus, the heterogeneity of the local surrounding. Models represent the transfer efficiencies of momentum and heat accurately while the prediction for CO2 and H2O mostly fails. Other factors, like the interplay between the activity of sources and sinks are more important and accordingly, the transfer efficiency of CO2 can be consulted to identify times or wind sectors where the source/sink regime is altered by e.g. photosynthetic activity. The inter-comparison of the transport characteristics of heat, CO2 and H2O leads to the assumption of scalar dissimilarity. By applying the quadrant analysis framework to the long-term time series, dominant turbulent structures responsible for efficient vertical exchange, i.e. coherent structures, can be identified. The length of the time series allows to extend the analysis to the stable range, which usually rarely occurs in urban areas. The variability of local urban rhoC is investigated in comparison to regional background concentration records. While patterns on daily and seasonal scales are similar, the vicinity to the ground sources of the local measurements leads to a stronger sensitivity to changes on small temporal scales. The height above ground of the background concentration measurements and thus the larger distance from the ground sources results in a phase shift of up to three months compared to the local seasonal course of rhoC. While rhoC in the urban area is also clearly elevated by 10 ppm on average, the behavior of rhoC in the urban environment reveals good consistency with background concentration measurements in terms of seasonality and long-term trend. The calculated local linear trend for the time period between 2005 and 2014 is around 2 ppm/y, which also coincides well with the global average trend. The coupling between FC and anthropogenic activity in the urban area is apparent from considerable differences in weekday and weekend fluxes, the diurnal cycle as a result of traffic volume or the seasonality caused by additional heating activity in wintertime. The variability of FC scales with the source activity and a long-term decrease of FC around 5% is observed locally as a result of a decrease in traffic activity during the investigation period. However, variabilities on all temporal scales are clearly larger than the observed long-term tendencies. For the investigation of FC in the heterogeneous urban environment an appropriate weighting between individual wind sectors is shown to be necessary due to the unequal frequency distribution of wind directions. The application of a refined methodology for the calculation of horizontally averaged fluxes of CO2 significantly improves the representativity of the data for the investigation area and also enhances the comparability of the data to results from other studies. The length of the current dataset allows to estimate the significance of the observed long-term behavior. While up to six years are potentially needed to calculate a significant inter-annual trend of rhoC, statistics of FC still benefit from even longer data records due to the larger variability. This gives evidence, that long-term time series of urban CO2 can help to add valuable knowledge to the current understanding of the urban ecosystem and its role in the global carbon balance

Slow and velocity-tunable beams of metastable He2_2 by multistage Zeeman deceleration

Metastable helium molecules (He$_2^*$) have been generated by striking a discharge in a supersonic expansion of helium gas from a pulsed valve. When operating the pulsed valve at room temperature, 77K, and 10K, the mean velocity of the supersonic beam was measured to be 1900m/s, 980m/s, and 530m/s, respectively. A 55-stage Zeeman decelerator operated in a phase-stable manner was then used to further reduce the beam velocity and tune it in the range between 100 and 150m/s. The internal-state distribution of the decelerated sample was established by photoionization spectroscopy.Comment: 10 pages, 7 figure

Invariance properties of random vectors and stochastic processes based on the zonoid concept

Two integrable random vectors ξ and ξ* in IRd are said to be zonoid equivalent if, for each u∈IRd, the scalar products 〈ξ,u〉 and 〈ξ*,u〉 have the same first absolute moments. The paper analyses stochastic processes whose finite-dimensional distributions are zonoid equivalent with respect to time shift (zonoid stationarity) and permutation of time moments (swap-invariance). While the first concept is weaker than the stationarity, the second one is a weakening of the exchangeability property. It is shown that nonetheless the ergodic theorem holds for swap invariant sequences and the limits are characterized

Maastricht 2.0: Eine neue Finanzregel für Europa = Maastricht 2.0: A new financial rule for Europe

No abstract