An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cram\'{e}r-Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures

Positive streamers are thought to propagate by photo-ionization whose parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in pure oxygen and argon. Our new experimental set-up guarantees contamination of the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to measure as they emit considerably less light in the sensitivity range of our fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all nitrogen/oxygen mixtures look generally similar, but become somewhat thinner and branch more with decreasing oxygen content. In pure nitrogen the streamers can branch so much that they resemble feathers. This feature is even more pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the feathers at 200 mbar; this density could be interpreted as the free electron density creating avalanches towards the streamer stem. It is remarkable that the streamer velocity is essentially the same for similar voltage and pressure in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen concentration and therefore the photo-ionization lengths vary by more than five orders of magnitude. Streamers in argon have essentially the same velocity as well. The physical similarity of streamers at different pressures is confirmed in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and spectra removed - subsection regarding effects of repetition frequency added - many more smaller change

Spatial coupling of particle and fluid models for streamers: where nonlocality matters

Particle models for streamer ionization fronts contain correct electron energy distributions, runaway effects and single electron statistics. Conventional fluid models are computationally much more efficient for large particle numbers, but create too low ionization densities in high fields. To combine their respective advantages, we here show how to couple both models in space. We confirm that the discrepancies between particle and fluid fronts arise from the steep electron density gradients in the leading edge of the fronts. We find the optimal position for the interface between models that minimizes computational effort and reproduces the results of a pure particle model.Comment: 4 pages, 5 figure

Spatiotemporally resolved imaging of streamer discharges in air generated in a wire-cylinder reactor with (sub)nanosecond voltage pulses

We use (sub)nanosecond high-voltage pulses to generate streamers in atmospheric-pressure air in a wire-cylinder reactor. We study the effect of reactor length, pulse duration, pulse amplitude, pulse polarity, and pulse rise time on the streamer development, specifically on the streamer distribution in the reactor to relate it to plasma-processing results. We use ICCD imaging with a fully automated setup that can image the streamers in the entire corona-plasma reactor. From the images, we calculate streamer lengths and velocities. We also develop a circuit simulation model of the reactor to support the analysis of the streamer development. The results show how the propagation of the high-voltage pulse through the reactor determines the streamer development. As the pulse travels through the reactor, it generates streamers and attenuates and disperses. At the end of the reactor, it reflects and adds to itself. The local voltage on the wire together with the voltage rise time determine the streamer velocities, and the pulse duration the consequent maximal streamer length