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

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

Optimal Management of Elective Joint Replacement Surgery in Patients with Hemophilia

Hemophilia is a genetic or acquired disease that leads to spontaneous and recurrent bleedings, which affect the joints and muscles, thus determining chronic damage to the cartilage which will lead to joint disease and hemophilic arthropathy. Even though hemophilic patients were initially thought to have a low incidence of atherothrombotic complications, it is now clear that atherothrombotic events occur. The administration of plasmatic factor VIII has better clinical results in type A hemophilic patients than the transfusion with plasma. We analyzed five patients with hemophilia type A, aged between 35 and 62 years. Two of them had a severe form of hemophilia with factor VIII less than 1%, while the other three had a moderate form with factor VIII ranging between 1 and 5%. The five patients underwent total knee repair interventions and received substitution treatment with clotting factors but also prophylactic anticoagulant treatment. The postsurgical evolution of these patients was favorable, with similar hemostatic profile as the non-hemophilic patients. Moroctocog alfa is an efficient substitutive treatment that manages to normalize the hemostatic profile of patients. Therefore, it is recommended to provide prophylactic antithrombotic therapy after the orthopedic interventions

Apparent close approaches between near-Earth asteroids and quasars. Precise astrometry and frame linking

Reproduced with permission. Copyright ESO. Article published by EDP Sciences and available at www.aanda.org.International audienceAims. We investigate the link between the International Celestial Reference Frame (ICRF) and the dynamical reference frame realized by the ephemerides of the Solar System bodies. Methods. We propose a procedure that implies a selection of events for asteroids with accurately determined orbits crossing the CCD field containing selected quasars. Using a Bulirsch-Stoer numerical integrator, we constructed 8-years (2010-2018) ephemerides for a set of 836 numbered near-Earth asteroids (NEAs). We searched for close encounters (within a typical field of view of groundbased telescopes) between our selected set of asteroids and quasars with high-accuracy astrometric positions extracted from the Large Quasars Astrometric Catalog (LQAC). Results. In the designated period (2010-2018), we found a number of 2924, 14 257, and 6972 close approaches (within 10') between asteroids with a minimum solar elongation value of 60◦and quasars from the ICRF-Ext2, the Very Large Baseline Array Calibrator Survey (VLBA-CS), and the Very Large Array (VLA), respectively. This large number of close encounters provides the observational basis needed to investigate the link between the dynamical reference frame and the ICRF

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model

Replication study of 34 common SNPs associated with prostate cancer in the Romanian population

Prostate cancer is the third‐most common form of cancer in men in Romania. The Romanian unscreened population represents a good sample to study common genetic risk variants. However, a comprehensive analysis has not been conducted yet. Here, we report our replication efforts in a Romanian population of 979 cases and 1027 controls, for potential association of 34 literature‐reported single nucleotide polymorphisms (SNPs) with prostate cancer. We also examined whether any SNP was differentially associated with tumour grade or stage at diagnosis, with disease aggressiveness, and with the levels of PSA (prostate specific antigen). In the allelic analysis, we replicated the previously reported risk for 19 loci on 4q24, 6q25.3, 7p15.2, 8q24.21, 10q11.23, 10q26.13, 11p15.5, 11q13.2, 11q13.3. Statistically significant associations were replicated for other six SNPs only with a particular disease phenotype: low‐grade tumour and low PSA levels (rs1512268), high PSA levels (rs401681 and rs11649743), less aggressive cancers (rs1465618, rs721048, rs17021918). The strongest association of our tested SNP's with PSA in controls was for rs2735839, with 29% increase for each copy of the major allele G, consistent with previous results. Our results suggest that rs4962416, previously associated only with prostate cancer, is also associated with PSA levels, with 12% increase for each copy of the minor allele C. The study enabled the replication of the effect for the majority of previously reported genetic variants in a set of clinically relevant prostate cancers. This is the first replication study on these loci, known to associate with prostate cancer, in a Romanian population.This study was funded in part by the European Union FP7 Program (ProMark project 202059) and by the EEA grant (ROMCAN project RO14-0017; EEA-JRP-RO-NO-20131-10191).Peer reviewe

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal