Stable solutions for optimal reinsurance problems involving risk measures

The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others.This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a “stable optimal retention” that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented.     

Determination of chlorinated toluenes in soils using gas chromatography tandem mass spectrometry

A method for the analysis of chlorotoluenes (CTs) in soil has been developed based on ultrasonic assisted extraction with a low volume of organic solvent and determination by gas chromatography-tandem mass spectrometry (GC–MS/MS). A simultaneous clean-up on an alumina–anhydrous sodium sulphate mixture was carried out to remove soil interferences. However, an additional clean-up with graphitised carbon was needed for some very dirty samples. Several solvents were assayed and a mixture of ethyl acetate:hexane (80?:?20, v/v) was selected to carry out soil extractions. Recovery studies were performed at 0.2, 0.1, 0.05 and 0.02?ng?g^?1 fortification levels, and recoveries obtained for all the compounds and concentrations were higher than 81% with standard deviations fulfilling the requirements of the IUPAC. LODs from 0.7 to 5.2?ng?kg^?1 and LOQs from 2.2 to 17.5?ng?kg^?1 were achieved for the analysed compounds, being pentachlorotoluene the compound with the highest limits, followed by the monochlorinated toluenes. The proposed analytical method was applied to determine CT levels in agricultural and industrial soils. These compounds were found in all the industrial soils analysed and some CTs were present in agricultural soils at lower levels.     

Local maximal function and weights in a general setting

For a proper open set $\Omega $ immersed in a metric space with the weak homogeneity property, and given a measure $\mu $ doubling on a certain family of balls lying “well inside” of $\Omega $ , we introduce a local maximal function and characterize the weights $w$ for which it is bounded on $L^p(\Omega ,w d\mu )$ when $1<p<\infty $ and of weak type $(1,1)$ . We generalize previous known results and we also present an application to interior Sobolev’s type estimates for appropriate solutions of the differential equation $\Delta ^m u=f$ , satisfied in an open proper subset $\Omega $ of $\mathbb R ^n$ . Here, the data $f$ belongs to some weighted $L^p$ space that could allow functions to increase polynomially when approaching the boundary of $\Omega $ .     

Ar+ ArH+ Reactive Collisions of Astrophysical Interest: The Case of 36Ar

The reactive collision between ³⁶Ar and the ³⁶ArH⁺ species has been investigated by means of quantum mechanical (QM), quasiclassical trajectories (QCT) and statistical quantum mechanical (SQM) approaches. Reaction probabilities, cross sections as a function of the energy and rate constants in terms of the temperature have been obtained. Cumulative distributions as a function of the collision time and the inspection of selected QCT corresponding to specific dynamical mechanisms have been analysed. Predictions by means of the SQM method are in good agreement with the QM results, thus supporting the complex-forming nature of the process.     

Substitutions of fluorine atoms and phenoxy groups in the synthesis of quinoxaline 1,4-di-N-oxide derivatives

The unexpected substitution of fluorine atoms and phenoxy groups attached to quinoxaline or benzofuroxan rings is described. The synthesis of 2-benzyl- and 2-phenoxy-3-methylquinoxaline 1,4-di-N-oxide derivatives was based on the classical Beirut reaction. The tendency of fluorine atoms linked to quinoxaline or benzofuroxan rings to be replaced by a methoxy group when dissolved in an ammonia saturated solution of methanol was clearly demonstrated. In addition, 2-phenoxyquinoxaline 1,4-di-N-oxide derivatives became 2-aminoquinoxaline 1,4-di-N-oxide derivatives in the presence of gaseous ammonia.     

Unexpected reduction of ethyl 3-phenylquinoxaline-2- carboxylate 1,4-di-N-oxide derivatives by amines

The unexpected tendency of amines and functionalized hydrazines to reduce ethyl 3-phenylquinoxaline-2-carboxylate 1,4-di-N-oxide (1) to afford a quinoxaline 1c and mono-oxide quinoxalines 1a and 1b is described. The experimental conditions were standardized to the use of two equivalents of amine in ethanol under reflux for two hours,with the aim of studying the distinct reductive profiles of the amines and the chemoselectivity of the process. With the exception of hydrazine hydrate, which reduced compound 1 to a 3-phenyl-2-quinoxalinecarbohydrazide derivative, the amines only acted as reducing agents.     

Physicochemical characterization of n-butyl-3-methylpyridinium dicyanamide [corrected] ionic liquid

The room temperature ionic liquid n-butyl-3-methylpyridinium dicyanamide has been characterized. Physicochemical properties such as density, speed of sound, refractive index, surface tension, and kinematic viscosity of the studied liquid have been experimentally measured in a wide range of temperatures. From results, coefficients of thermal expansion, molar refractions, dynamic viscosities and entropies and enthalpies of surface formation per unit surface area at the studied temperatures have been derived. We have analyzed the achieved results for evaluating the effect of the anionic structure in these properties, getting interesting results which lead us to a better understanding of the behavior of the ions in the fluids. Moreover, thermal properties of several pyridinium-based ionic liquids have been investigated. Finally, from both dynamic viscosity values and glass transition temperature of the studied liquids, a detailed analysis of the behavior in fragility terms has been performed.     

Thermophysic comparative study of two isomeric pyridinium-based ionic liquids

A comprehensive thermophysical study of isomeric room-temperature ionic liquids n-butyl-3-methyl-pyridinium tetrafluoroborate and n-butyl-4-methyl-pyridinium tetrafluoroborate has been performed. This paper reports various experimental data including density, speed of sound, refractive index, surface tension, isobaric molar heat capacity, and kinematic viscosity. From the experimental results, coefficients of thermal expansion, dynamic viscosities and molar refractions of the studied ionic liquids have been determined. Results have been analyzed paying special attention to the different features of the isomers and their structural differences. Several theories and empirical relations have been applied in order to predict physical properties of ionic liquids. A good agreement between experimental and calculated data has been found. Furthermore, a study about the versatility and application of the different relationships has been carried out finding that in general density and coefficients of thermal expansion can be estimated with relatively good accuracy.     

Copper release kinetics from a long-term contaminated acid soil using a stirred flow chamber: effect of ionic strength and pH

The effect of pH and ionic strength on copper release in a long-term Cu-polluted soil was studied using a stirred flow chamber. The presence of Ca(2+) and Na(+) was also evaluated. More copper was released as the ionic strength increased, and it was significantly higher in the presence of Ca(2+) than in the presence of Na(+). The maximum amount of Cu that could be released under experimental conditions increased logarithmically as the ionic strength increased, and the release rate parameters were not significantly correlated with ionic strength values. The maximum amount of Cu that could be released was similar for solutions with pH values between 5.5 and 8.5. For solutions with a pH value below 4.5, the amount of Cu released increased exponentially as the pH decreased. The release rate parameters and Cu release pattern were affected by pH, especially for more acidic solutions (pH values of 2.5 and 3.5).     

Towards β-selectivity in functional estrogen receptor antagonists

Based on the benzo[b]naphtho[1,2-d]furan and benzo[b]naphtho[1,2-d]thiophene frameworks, a series of ligands with different basic side chains (BSCs) has been synthesized and pharmacologically evaluated. Also, their binding modes have been modelled using docking techniques. It was found that the introduction of a BSC in these systems brings about a decrease of affinity for both estrogen receptors α and β in an in vitro competitive binding assay. However, two full antagonists of the estrogen receptor β ( and ) have been discovered, with potency in the low micromolar concentration in a cell-based luciferase reporter assay, and completely devoid of activity against the α receptor at the same concentration range. Differences in the ERα/ERβ binding modes have also been rationalized with the help of molecular modelling techniques. This interesting functional profile could be used to elucidate the physiological role of each ER subtype.