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We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a numerical method for its solution. We show weak convergence of an approximating sequence of piecewise-deterministic Markov processes (PDMPs) for deriving the convergence of the procedures. We will use estimated PDMP characteristics in a subsequent step from simulated sample data and study its effect on the numerically computed Gerber-Shiu functions. It can be seen that the main source of instability stems from the hazard rate estimator. Interestingly, results obtained using MC methods are hardly affected by estimation.

In order to gain a systematic understanding of electrode/electrolyte interface between gold electrodes and ionic liquids, the adsorption of 1-butyl-3-methyl-imidazolium-hexafluorophosphate (BMI/PF $$_6$$ ) on Au(100) was determined for a wide range of surface coverages using density functional theory (DFT) calculations. At low coverages BMI is exceptionally mobile (translational and rotational barriers of $$

We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding (subject to some proportional transaction costs). For modelling dividends we use the common approach whereas for the funding opportunity we use the jump times of another independent Poisson process at which we choose an appropriate funding height. In case of exponentially distributed claims we are able to determine an explicit solution to the problem and derive an optimal strategy whose nature heavily depends on the size of the transaction costs. Furthermore, the optimal strategy identifies unfavourable surplus positions prior to ruin at which refunding is highly recommended.

Current progress in modern electrocatalysis research is spurred by theory, frequently based on ab initio thermodynamics, where the stable reaction intermediates at the electrode surface are identified, while the actual energy barriers are ignored. This approach is popular in that a simple tool is available for searching for promising electrode materials. However, thermodynamics alone may be misleading to assess the catalytic activity of an electrochemical reaction as we exemplify with the chlorine evolution reaction (CER) over a RuO2 (110) model electrode. The full procedure is introduced, starting from the stable reaction intermediates, computing the energy barriers, and finally performing microkinetic simulations, all performed under the influence of the solvent and the electrode potential. Full kinetics from first-principles allows the rate-determining step in the CER to be identified and the experimentally observed change in the Tafel slope to be explained.

Motivated by our previous studies on metallic substrates, in the present work we addressed the functionalization and the subsequent metallization of a hydrogen-terminated n-Si(111) electrode. DFT provides atomistic insights on the grafting mechanism of 4-pyridinecarboxaldehyde (C6H5NO) what encouraged electrochemical investigations, i. e. cyclic voltammetry and in-situ STM, combined with XPS measurements which together provide evidence for a successful transfer of the so far obtained knowledge from metal single crystal to semiconductor surfaces.

We describe a multiscale modeling hierarchy for the particular case of Au-island ripening on Au(100). Starting at the microscopic scale, density functional theory was used to investigate a limited number of self-diffusion processes on perfect and imperfect Au(100) surfaces. The obtained structural and energetic information served as basis for optimizing a reactive forcefield (here ReaxFF), which afterwards was used to address the mesoscopic scale. Reactive force field simulations were performed to investigate more diffusion possibilities at a lower computational cost but with similar accuracy. Finally, we reached the macroscale by means of kinetic Monte Carlo (kMC) simulations. The reaction rates for the reaction process database used in the kMC simulations were generated using the reactive force field. Using this strategy, we simulated nucleation, aggregation, and fluctuation processes for monoatomic high islands on Au(100) and modeled their equilibrium shape structures. Finally, by calculating the step line tension at different temperatures, we were able to make a direct comparison with available experimental data.