Recursive methods for a multi-dimensional risk process with common shocks

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber-Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end. © 2011 Elsevier B.V.postprin

Romanian 14 GHz ECR Ion Source RECRIS: main features and first operation

RECRIS, the romanian 14 GHz ECR ion source, designed to be used as a facility for atomic physics and material studies with highly charged ion beams, have been recently completed. The general design [1], the main characteristics and the detailed measurements of the radial [2] and axial magnetic fields are presented. A maximum axial magnetic field of 1.4 T and a mirror ratio of up to 4 were obtained. The dependence of the mirror ratio and of the ECR plasma zone volume on the configuration of the axial magnetic system configuration was studied. The first operation of this source is described, showing a good stability

Optical Spin Initialization and Non-Destructive Measurement in a Quantum Dot Molecule

The spin of an electron in a self-assembled InAs/GaAs quantum dot molecule is optically prepared and measured through the trion triplet states. A longitudinal magnetic field is used to tune two of the trion states into resonance, forming a superposition state through asymmetric spin exchange. As a result, spin-flip Raman transitions can be used for optical spin initialization, while separate trion states enable cycling transitions for non-destructive measurement. With two-laser transmission spectroscopy we demonstrate both operations simultaneously, something not previously accomplished in a single quantum dot.Comment: Accepted for publication in Phys. Rev. Let

Claim Reserving via Inverse Probability Weighting: A Micro-Level Chain-Ladder Method

Claim reserving is primarily accomplished using macro-level models, with the Chain-Ladder method being the most widely adopted method. These methods are usually constructed heuristically and rely on oversimplified data assumptions, neglecting the heterogeneity of policyholders, and frequently leading to modest reserve predictions. In contrast, micro-level reserving leverages on stochastic modeling with granular information for improved predictions, but usually comes at the cost of more complex models that are unattractive to practitioners. In this paper, we introduce a simple macro-level type approach that can incorporate granular information from the individual level. To do so, we imply a novel framework in which we view the claim reserving problem as a population sampling problem and propose a reserve estimator based on inverse probability weighting techniques, with weights driven by policyholders' attributes. The framework provides a statistically sound method for aggregate claim reserving in a frequency and severity distribution-free fashion, while also incorporating the capability to utilize granular information via a regression-type framework. The resulting reserve estimator has the attractiveness of resembling the Chain-Ladder claim development principle, but applied at the individual claim level, so it is easy to interpret and more appealing to practitioners

A two-dimensional risk model with proportional reinsurance

In this paper we consider an extension of the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008a). To this end, we assume that there are two insurers. The first insurer is subject to claims arising from two independent compound Poisson processes. The second insurer, which can be viewed as a different line of business of the same insurer or as a reinsurer, covers a proportion of the claims arising from one of these two compound Poisson processes. We derive the Laplace transform of the time until ruin of at least one insurer when the claim sizes follow a general distribution. The surplus level of the first insurer when the second insurer is ruined first is discussed at the end in connection with some open problems. © Applied Probability Trust 2011.postprin

Metal-dielectric structures for high charge state ion production in ECR plasma

Metal-dielectric (MD) structures of pure (99.999%) aluminum foils were previously studied [1, 2] in the National Institute for Physics and Nuclear Engineering (NIPNE), Bucharest, Romania showing high secondary electron emission properties. Consequently, 26 mm diameter disks of such structures (Al-Al2O3) were tested in the ECR ion source of the Institut fuer Kernphysik (IKF) der J. W. Goethe Universitat, Frankfurt/Main, Germany, allowing to demonstrate their ability to significantly increase the ECRIS performances in what concerns the production of high charge state ions [3]. New experiments carried on in Bucharest on a special facility [2] stressed out the possibility to develop high emissive MD structures starting from lower purity (99%) aluminum foils. This result allowed us to make a special cylinder of 1 mm wall thickness electrolytically treated so that only the inner face had a MD structure layer while the external surface remained metallic. Such a cylinder introduced in the plasma chamber of an ECR ion source provides a high rate of secondary electrons that enhance the ECR plasma electron density while its metallic external surface provides a good electric and thermal contact with the plasma chamber. The tests performed with such a MD aluminum cylinder in the IKF 14 GHz ECR ion source, successfully demonstrated the possibility to shift the ECRIS output toward very high charge states (Ar16+) due to the strong secondary electron emission of the MD inner surface of the cylinder

Data Mining of Telematics Data: Unveiling the Hidden Patterns in Driving Behaviour

With the advancement in technology, telematics data which capture vehicle movements information are becoming available to more insurers. As these data capture the actual driving behaviour, they are expected to improve our understanding of driving risk and facilitate more accurate auto-insurance ratemaking. In this paper, we analyze an auto-insurance dataset with telematics data collected from a major European insurer. Through a detailed discussion of the telematics data structure and related data quality issues, we elaborate on practical challenges in processing and incorporating telematics information in loss modelling and ratemaking. Then, with an exploratory data analysis, we demonstrate the existence of heterogeneity in individual driving behaviour, even within the groups of policyholders with and without claims, which supports the study of telematics data. Our regression analysis reiterates the importance of telematics data in claims modelling; in particular, we propose a speed transition matrix that describes discretely recorded speed time series and produces statistically significant predictors for claim counts. We conclude that large speed transitions, together with higher maximum speed attained, nighttime driving and increased harsh braking, are associated with increased claim counts. Moreover, we empirically illustrate the learning effects in driving behaviour: we show that both severe harsh events detected at a high threshold and expected claim counts are not directly proportional with driving time or distance, but they increase at a decreasing rate

A Posteriori Risk Classification and Ratemaking with Random Effects in the Mixture-of-Experts Model

A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk profile. In this paper, we propose to adapt a flexible regression model, called the Mixed LRMoE, to the problem of a posteriori risk classification and ratemaking, where policyholder-level random effects are incorporated to better infer their risk profile reflected by the claim history. We also develop a stochastic variational Expectation-Conditional-Maximization algorithm for estimating model parameters and inferring the posterior distribution of random effects, which is numerically efficient and scalable to large insurance portfolios. We then apply the Mixed LRMoE model to a real, multiyear automobile insurance dataset, where the proposed framework is shown to offer better fit to data and produce posterior premium which accurately reflects policyholders' claim history