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

Rilevamento di ozono presso i siti forestali UN/ECE Level I nella Provincia di Trento nel 2007

A causa del suo alto potere ossidante, dei suoi elevati livelli e della sua ampia diffusione in aree rurali e forestali, l’ozono troposferico (O3) è ritenuto il contaminante gassoso di potenziale maggiore pericolosità per la vegetazione agraria, semi-naturale e forestale. L’obiettivo del presente studio è ottenere stime realistiche dell’esposizione ad O3 della vegetazione forestale della provincia di Trento, essenziali per poter valutare se siano ipotizzabili effetti di questo inquinante sulla vegetazione. A tale scopo sono stati installati 15 siti di misura delle concentrazioni di O3, riferendosi ai punti della rete UE e UN/ECE di monitoraggio delle foreste di Livello I della provincia di Trento; l’ozono è stato misurato utilizzando campionatori passivi, che forniscono un dato settimanale, successivamente convertito in valori di concentrazione media oraria. L’affidabilità dei dati ottenuti è stata verificata per confronto con i dati forniti in parallelo da centraline automatiche. Le concentrazioni medie settimanali di O3 rilevate nel periodo 6 giugno - 19 settembre 2007 sono risultate comprese tra 62.4±12.4 e 130.6±22.3 μg*m-3. In termini di AOT40, l’indicatore di rischio utilizzato dalla normativa UE e dall’UN/ECE, i valori sono tali da prefigurare frequenti superamenti dei livelli critici nel corso della stagione estiva 2007. Si discutono nel dettaglio andamenti spaziali e temporali dei dati raccolti e si ipotizza una linea futura per la prosecuzione del lavoro nell’ottica di una maggiore comprensione del fenomeno

Bioindication of troposheric ozone by native vegetation: the potential of Viburnum lantana for large-scale surveys

Tropospheric ozone is one of the most important phytotoxic air pollutant. Biomonitoring by native plants is an option when the assessment of its impact on vegetation in large-scale surveys and in remote areas is of concern. The shrub species Viburnum lantana L. (wayfaring tree) is known to be sensitive to ozone, develops specific symptoms consisting in red stipples on the upper surface, and has a wide spatial distribution. However it is not fully known if it meets all the requirements to be used as an in situ bioindicator (Doley, 2010). In particular, the actual responsiveness to ozone of native plants and the relationship between the intensity of responses and the levels of exposure to the pollutant under field conditions remain to be evaluated. For these purposes, two field studies were carried out in Trentino (North Italy) at local (1) and large scale (2). (1) Firstly, at local level, we considered two 1x1 km quadrates characterized by different ozone levels. A fully randomized design was adopted to ensure within-quadrate replications and to select V. lantana plants for the monitoring of ozone-specific foliar symptoms development, the chlorophyll (Chl) content and the fluorescence of Chl a during the entire growing season. (2) Secondly, a stratified (elevation x ozone) random design was used to test the response of V. lantana in terms of symptomatic plant percentage at larger scale (6200 km2). Overall, the results of the two field studies allowed to verify a temporal development of the responses of V. lantana consistent with the trend of ozone exposure (Gottardini et al., 2010), and an higher frequency of symptomatic plants where ozone levels were also higher. However, the frequency of symptoms was not always proportionate to the level of ozone exposure. At the same time of the onset and spread of foliar symptoms, a decrease in the foliar Chl content and in photosynthetic performance occurred. V. lantana seems suitable as a bioindicator in situ to qualitatively assess the potential impact of ozone

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

Solid-phase extraction of vanadium(V) from teainfusions and wines on immobilized nanometer titanium dioxide followed by ICP-OES analysis

Nanosized titanium dioxide immobilized on silica gel was synthesized and used as fixedbed phase for V(V) pre-concentration, followed by inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis. Three different sorbents were prepared by sol\u2013gel method starting from a mixture of titanium isopropoxide, 2-propanol and water, and characterized by X-ray powder diffraction (XRPD), scanning electron microscopy (SEM) and BET analysis. V(V), the most stable and toxic oxidation state of the element, present in water and beverages samples, was selectively sorbed, pre-concentrated, quantitatively eluted by 0.1 M HCl and analyzed by ICP-OES. The effectiveness of the procedure was first assessed on tap water enriched with 1 lg L1 of V(V) obtaining recoveries up to 92% (n= 4). The pre-concentration step was then optimized for complex matrices such as tea infusions and red and white wines. The reliability of the procedure was assessed on the same beverages samples spiked with 20\u2013250 lg L1. Quantitative recoveries (82\u2013 95%, n= 4) were assured avoiding any sample pre-treatment, generally essential in such complex matrices, obtaining good precision (RSD< 12%, n= 3). The method was then applied to the determination of V(V) in commercial tea infusions and wines