We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank-dependent expected utility (RDEU) theory with a concave utility function and an inverse-S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave. KEY WORDS: optimal insurance design, rank-dependent expected utility, inverse-S shaped probability distortion, indemnity, quantile formulation, deductible.

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Regenerable, multifunctional ebselenol antioxidants were prepared that could quench peroxyl radicals more efficiently than α-tocopherol. These compounds act as better mimics of the glutathione peroxidase enzymes than ebselen. Production of reactive oxygen species (ROS) and reactive nitrogen species (RNS) in human mononuclear cells was considerably decreased upon exposure to the organoselenium compounds. At a concentration of 25 μm, the ebselenol derivatives showed minimal toxicity in pre-osteoblast MC3T3 cells.

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Novel azo-bis-ebselen compounds 7 were prepared by reduction of 7-nitro-2-aryl-1,2-benzisoselenazol-3(2H)-ones 3 and 6 with sodium benzenetellurolate, NaTeC6H5, and by reaction of 2-bromo-3-nitrobenzamides with Na2Se2. The X-ray structure of 7b showed that the molecule, due to strong intramolecular secondary Se···N interactions, is completely planar. Azo-compounds 7 upon further reaction with NaTeC6H5 were reductively cleaved to provide two equivalents of the corresponding aromatic amine. The weak Se─N bond was not stable enough to survive the reaction conditions and diselenides 8 were isolated after work-up. Whereas azo-bis-ebselens 7 were poor mimics of the glutathione peroxidase (GPx)-enzymes, nitroebselens 3, 6 and 11b and diselenides 8 were 3-6 fold more active than ebselen. Based on 77 Se NMR spectroscopy, a catalytic cycle for diselenide 8b, involving aminoebselen 14, was proposed. As assessed by chemiluminescence measurements, the good GPx-mimics could reduce production of reactive oxygen species (ROS) in stimulated human mononuclear cells more efficiently than Trolox. No toxic effects of the compounds were seen in MC3T3-cells at 25 M.