Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails

We consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction as well as the efficiency gain of our method over another fast standard technique based on the classical Pollaczek-Khinchine formula. We provide a numerical example to illustrate the performance, and show that for more time-consuming conditional Monte Carlo techniques, the new series representation also does not compare unfavorably to the one based on the Pollaczek-Khinchine formula.

     

Zur Adsorption von Olefinmolekülen in Zeolithen

The interaction between 1-olefine molecules and Na⁺ ions in zeolites of type NaY were studied by¹³C NMR spectroscopy and quantum chemical calculations. Characteristic chemical shifts of olefinic carbon atoms indicate a terminal arrangement of the cation near the olefinic part of the molecule.

     

La9Sb16Br3 and Ce9Sb16Cl3: stars and stripes in rare earth halide and intermetallic compounds

The title compounds were synthesized from Ln, LnX(3) (Ln = La, Ce; X = Cl, Br), and Sb under an Ar atmosphere at 950 degrees C. They crystallize in the space group P6(3)/m (No. 176) with lattice constants a = 21.232(5) and 20.862(2) Angstroms and c = 4.323(2) and 4.2728(7) Angstroms for La(9)Sb(16)Br(3) and Ce(9)Sb(16)Cl(3), respectively. The solids are the most metal-rich members in the reduced rare earth metal halide family and contain partial structures which are characteristic of reduced halides and intermetallic phases. These are the [Ln(6)X(6)](infinity) hexagon stars, Sb-centered [Ln(3)Sb](infinity) trigonal prismatic columns, and stripes of Sb square meshes. Computational analysis indicates that their electronic structure is valence-precise in the reduced halide part, but electron-deficient in the intermetallic part. Susceptibility and resistivity measurements reveal the metallic nature of the compounds.     

Isomerization and fragmentation reactions of gaseous phenylarsane radical cations and phenylarsanyl cations. A study by tandem mass spectrometry and theoretical calculations

The unimolecular reactions of radical cations and cations derived from phenylarsane, C6H5AsH2 (1) and dideutero phenylarsane, C6H5AsD2 (1-d2), were investigated by methods of tandem mass spectrometry and theoretical calculations. The mass spectrometric experiments reveal that the molecular ion of phenylarsane, 1*+, exhibits different reactivity at low and high internal excess energy. Only at low internal energy the observed fragmentations are as expected, that is the molecular ion 1*+ decomposes almost exclusively by loss of an H atom. The deuterated derivative 1-d2 with an AsD2 group eliminates selectively a D atom under these conditions. The resulting phenylarsenium ion [C6H5AsH]+, 2+, decomposes rather easily by loss of the As atom to give the benzene radical cation [C6H6]*+ and is therefore of low abundance in the 70 eV EI mass spectrum. At high internal excess energy, the ion 1*+ decomposes very differently either by elimination of an H2 molecule, or by release of the As atom, or by loss of an AsH fragment. Final products of these reactions are either the benzoarsenium ion 4*+, or the benzonium ion [C6H7]+, or the benzene radical cation, [C6H6]*+. As key-steps, these fragmentations contain reductive eliminations from the central As atom under H-H or C-H bond formation. Labeling experiments show that H/D exchange reactions precede these fragmentations and, specifically, that complete positional exchange of the H atoms in 1*+ occurs. Computations at the UMP2/6-311+G(d)//UHF/6-311+G(d) level agree best with the experimental results and suggest: (i) 1*+ rearranges (activation enthalpy of 93 kJ mol(-1)) to a distinctly more stable (DeltaH(r)(298) = -64 kJ mol(-1)) isomer 1 sigma*+ with a structure best represented as a distonic radical cation sigma complex between AsH and benzene. (ii) The six H atoms of the benzene moiety of 1 sigma*+ become equivalent by a fast ring walk of the AsH group. (iii) A reversible isomerization 1+<==>1 sigma*+ scrambles eventually all H atoms over all positions in 1*+. The distonic radical cation 1*+ is predisposed for the elimination of an As atom or an AsH fragment. The calculations are in accordance with the experimentally preferred reactions when the As atom and the AsH fragment are generated in the quartet and triplet state, respectively. Alternatively, 1*(+) undergoes a reductive elimination of H2 from the AsH2 group via a remarkably stable complex of the phenylarsandiyl radical cation, [C6H5As]*+ and an H2 molecule.