What do distortion risk measures tell us on excess of loss reinsurance with reinstatements ?

In this paper we focused our attention to the study of an excess of loss reinsurance with reinstatements, a problem previously studied by Sundt [5] and, more recently, by Mata [4] and HÄurlimann [3]. As it is well-known, the evaluation of pure premiums requires the knowledge of the claim size distribution of the insurance risk: in order to face this question, different approaches have been followed in the actuarial literature. In a situation of incomplete information in which only some characteristics of the involved elements are known, it appears to be particularly interesting to set this problem in the framework of risk adjusted premiums. It is shown that if risk adjusted premiums satisfy a generalized expected value equation, then the initial premium exhibits some regularity properties as a function of the percentages of reinstatement.Excess of loss reinsurance, reinstatements, distortion risk measures, expected value equation

On Bounds for Concave Distortion Risk Measures for Sums of Risks

In this paper we consider the problem of studying the gap between bounds of risk measures for sums of non-independent random variables. Owing to the choice of the context where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure of a discrete risk by referring to its writing as sum of layers. Then, we examine the case of sums of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. Finally, the attention is devoted to the analysis of the gap between risk measures of upper and lower bounds, with the aim of optimizing it.Distortion risk measures, discrete risks, concave risk measure, upper and lower bounds, gap between bounds

Distortion Risk Measures and Discrete Risks

In this paper we consider the problem of determining approximations for distortion risk measures of sums of non-independent random variables. First, we give an overview of the recent actuarial literature on distortion risk measures and convex bounds for sums of random variables. Then, we examine the case of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. The result is then extended to cover the case of non necessarily discrete risks.Risk measures; dependency of risks; discrete risks with identical distribution; upper and lower bounds: concave risk measures.

Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements

With reference to risk adjusted premium principle, in this paper we study excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution. In particular, we focus our study on conditions ensuring feasibility of the initial premium, for example with reference to the limit on the payment of each claim. Comonotonic exchangeability shows the way forward to a more general definition of the initial premium: some properties characterizing the proposed premium are presented.Excess of loss reinsurance; reinstatements; distortion risk measures; initial premium; exchangeability.

On Optimal Layer Reinsurance Model

In this paper, we consider the class of non-proportional reinsurance contracts known as layer reinsurance model or limited stop-loss treaty. With the aim of finding an optimal layer reinsurance, we make the choice of considering an optimization criteria preserving stop-loss order: we derive some conditions of optimality by minimizing insurer risk exposure under a generic concave distortion risk measure

On Optimal Reinsurance with Stochastic Premium

In this paper we study optimal reinsurance models from the per- spective of an insurer by minimizing the total risk exposure under a distortion risk measure in the hypothesis of a stochastic reinsurance premium. This assumption is consistent with reinsurance practice in which reinsurance premiums frequently depend on the recorded claims rate, therefore a random component results. For example, it is consis- tent with reinstatement clauses which are widely used in the industry

Nonconvulsive Seizures and Dementia: A Case Report

Nonconvulsive status epilepticus (NCSE) is a severe medical condition that shows increased incidence in the elderly and is frequently underdiagnosed because of its pleomorphic presentation. We report an NCSE in a 76-year-old woman affected by dementia with acute change of cognitive status and behavior. Intravenous diazepam solved clinical and electroencephalographic manifestations. Neuropsychological assessment after NCSE conclusion showed impairment of several fields that remained unchanged at 3-month followup. NCSE should be considered when sudden and transient cognitive fluctuations appear in the elderly. Epileptic events in dementia occur frequently and are often underrecognized; this could be a misleading factor when considering a quick progression of mnesic performances. Moreover, recent findings both in animal models and in humans demonstrated the deep link between epilepsy and dementia, also supporting the hypothesis that epileptiform activity could contribute to cognitive impairment

Long-term monitoring for the surveillance of the conservation status of Tursiops truncatus in an EU Natura2000 site in the Mediterranean Sea. A pilot study in the Tuscan Archipelago

A pilot study, using the dataset from the research network ‘FLT Med Net’, which regularly monitors transborder regions in the Mediterranean Sea using ferries as platform for systematic surveys, was undertaken to assess common bottlenose dolphin range and population trends within the Natura 2000 EU marine site “Tutela del Tursiops truncatus”. The site was recently designated by the Tuscany Region (Italy) within the requirement of the EU Habitats Directive. In order to evaluate the conservation status of bottlenose dolphin according to the surveillance scheme of the Directive, two six-year periods (2007-2012; 2013-2018) were compared to assess trends in distribution-occurrence (range); Sightings Per Unit of Effort and Density (population). In total, 18146 NM were surveyed along two fixed transects, recording 90 sightings of Tursiops truncatus and a total of 268 specimens. Between the two periods, slight but not statistically significant differences were assessed, with decreasing trend in range and population  of the species; no variation was detected in mean group sizes. Travelling was the most common behaviour, and juveniles were present in 20% of the sightings, concentrated during spring and summer. The consistent FLT Med Net dataset was found to be appropriate to evaluate important parameters for the assessment of trends in the conservation status of Tursiops truncatus at the Natura2000 site scale.

Essential Oil from Origanum vulgare Completely Inhibits the Growth of Multidrug-Resistant Cystic Fibrosis Pathogens.

Essential oils (EOs) are known to inhibit the growth of a wide range of microorganisms. Particularly interesting is the possible use of EOs to treat multidrug-resistant cystic fibrosis (CF) pathogens. We tested the essential oil (EO) from Origanum vulgare for in vitro antimicrobial activity, against three of the major human opportunistic pathogens responsible for respiratory infections in CF patients; these are methicillin-resistant Staphylococcus aureus, Stenotrophomonas maltophilia and Achromobacter xylosoxidans. Antibiotic susceptibility of each strain was previously tested by the standard disk diffusion method. Most strains were resistant to multiple antibiotics and could be defined as multi-drug-resistant (MDR). The antibacterial activity of O. vulgare EO (OEO) against a panel of 59 bacterial strains was evaluated, with MIC and MBC determined at 24, 48 and 72 hours by a microdilution method. The OEO was effective against all tested strains, although to a different extent. The MBC and MIC of OEO for S. aureus strains were either lower or equal to 0.50%, v/v, for A. xylosoxidans strains were lower or equal to 1% and 0.50%, v/v, respectively; and for S. maltophilia strains were lower or equal to 0.25%, v/v. The results from this study suggest that OEO might exert a role as an antimicrobial in the treatment of CF infections

Impact of trans-stent gradient on outcome after PCI: results from a HAWKEYE substudy

To test whether quantitative flow ratio (QFR)-based trans-stent gradient (TSG) is associated with adverse clinical events at follow-up. A post-hoc analysis of the multi-center HAWKEYE study was performed. Vessels post-PCI were divided into four groups (G) as follows: G1: QFR >= 0.90 TSG = 0 (n = 412, 54.8%); G2: QFR >= 0.90, TSG > 0 (n = 216, 28.7%); G3: QFR < 0.90, TSG = 0 (n = 37, 4.9%); G4: QFR < 0.90, TSG > 0 (n = 86, 11.4%). Cox proportional hazards regression model was used to analyze the effect of baseline and prognostic variables. The final reduced model was obtained by backward stepwise variable selection. Receiver operating characteristic (ROC) was plotted and area under the curve (AUC) was calculated and reported. Overall, 449 (59.8%) vessels had a TSG = 0 whereas (40.2%) had TSG > 0. Ten (2.2%) vessel-oriented composite endpoint (VOCE) occurred in vessels with TSG = 0, compared with 43 (14%) in vessels with TSG > 0 (p < 0.01). ROC analysis showed an AUC of 0.74 (95% CI: 0.67 to 0.80; p < 0.001). TSG > 0 was an independent predictor of the VOCE (HR 2.95 [95% CI 1.77-4.91]). The combination of higher TSG and lower final QFR (G4) showed the worst long-term outcome while low TSG and high QFR showed the best outcome (G1) while either high TSG or low QFR (G2, G3) showed intermediate and comparable outcomes. Higher trans-stent gradient was an independent predictor of adverse events and identified a subgroup of patients at higher risk for poor outcomes even when vessel QFR was optimal (> 0.90)