Calculation of solvency capital requirements for non-life underwriting risk using generalized linear models

The paper presents various GLM models using individual rating factors to calculate the solvency capital requirements for non-life underwriting risk in insurance. First, we consider the potential heterogeneity of claim frequency and the occurrence of large claims in the models. Second, we analyse how the distribution of frequency and severity varies depending on the modelling approach and examine how they are projected into SCR estimates according to the Solvency II Directive. In addition, we show that neglecting of large claims is as consequential as neglecting the heterogeneity of claim frequency. The claim frequency and severity are managed using generalized linear models, that is, negative-binomial and gamma regression. However, the different individual probabilities of large claims are represented by the binomial model and the large claim severity is managed using generalized Pareto distribution. The results are obtained and compared using the simulation of frequency-severity of an actual insurance portfolio.Web of Science26446645

Adiabatic two-qubit gates in capacitively coupled quantum dot hybrid qubits

The ability to tune qubits to flat points in their energy dispersions ("sweet spots") is an important tool for mitigating the effects of charge noise and dephasing in solid-state devices. However, the number of derivatives that must be simultaneously set to zero grows exponentially with the number of coupled qubits, making the task untenable for as few as two qubits. This is a particular problem for adiabatic gates, due to their slower speeds. Here, we propose an adiabatic two-qubit gate for quantum dot hybrid qubits, based on the tunable, electrostatic coupling between distinct charge configurations. We confirm the absence of a conventional sweet spot, but show that controlled-Z (CZ) gates can nonetheless be optimized to have fidelities of $\sim$99% for a typical level of quasistatic charge noise ($\sigma_\varepsilon$$\simeq$1 $\mu$eV). We then develop the concept of a dynamical sweet spot (DSS), for which the time-averaged energy derivatives are set to zero, and identify a simple pulse sequence that achieves an approximate DSS for a CZ gate, with a 5$\times$ improvement in the fidelity. We observe that the results depend on the number of tunable parameters in the pulse sequence, and speculate that a more elaborate sequence could potentially attain a true DSS.Comment: 14 pages, 9 figure

Excess of loss reinsurance under joint survival optimality

Explicit expressions for the probability of joint survival up to time x of the cedent and the reinsurer, under an excess of loss reinsurance contract with a limiting and a retention level are obtained, under the reasonably general assumptions of any non-decreasing premium income function, Poisson claim arrivals and continuous claim amounts, modelled by any joint distribution. By stating appropriate optimality problems, we show that these results can be used to set the limiting and the retention levels in an optimal way with respect to the probability of joint survival. Alternatively, for fixed retention and limiting levels, the results yield an optimal split of the total premium income between the two parties in the excess of loss contract. This methodology is illustrated numerically on several examples of independent and dependent claim severities. The latter are modelled by a copula function. The effect of varying its dependence parameter and the marginals, on the solutions of the optimality problems and the joint survival probability, has also been explored

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Antigen Uptake during Different Life Stages of Zebrafish (Danio rerio) Using a GFP-Tagged Yersinia ruckeri

Immersion-vaccines (bacterins) are routinely used for aquacultured rainbow trout to protect against Yersinia ruckeri (Yr). During immersion vaccination, rainbow trout take up and process the antigens, which induce protection. The zebrafish was used as a model organism to study uptake mechanisms and subsequent antigen transport in fish. A genetically modified Yr was developed to constitutively express green fluorescent protein (GFP) and was used for bacterin production. Larval, juvenile and adult transparent zebrafish (tra:nac mutant) received a bath in the bacterin for up to 30 minutes. Samples were taken after 1 min, 15 min, 30 min, 2 h, 12 h and 24 h. At each sampling point fish were used for live imaging of the uptake using a fluorescence stereomicroscope and for immunohistochemistry (IHC). In adult fish, the bacterin could be traced within 30 min in scale pockets, skin, oesophagus, intestine and fins. Within two hours post bath (pb) Yr-antigens were visible in the spleen and at 24 h in liver and kidney. Bacteria were associated with the gills, but uptake at this location was limited. Antigens were rarely detected in the blood and never in the nares. In juvenile fish uptake of the bacterin was seen in the intestine 30 min pb and in the nares 2 hpb but never in scale pockets. Antigens were detected in the spleen 12 hpb. Zebrafish larvae exhibited major Yr uptake only in the mid-intestine enterocytes 24 hpb. The different life stages of zebrafish varied with regard to uptake locations, however the gut was consistently a major uptake site. Zebrafish and rainbow trout tend to have similar uptake mechanisms following immersion or bath vaccination, which points towards zebrafish as a suitable model organism for this aquacultured species

Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student's copula, cannot be rejected if it has sufficiently many ``degrees of freedom''. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the correlation coefficient between the pair of asset is too high as the tail dependence neglected by the Gaussian copula can be as large as 0.6, i.e., three out five extreme events which occur in unison are missed.Comment: Latex document of 43 pages including 14 eps figure