Excess of loss reinsurance under joint survival optimality

Explicit expressions for the probability of joint survival up to time x of the cedent and the reinsurer, under an excess of loss reinsurance contract with a limiting and a retention level are obtained, under the reasonably general assumptions of any non-decreasing premium income function, Poisson claim arrivals and continuous claim amounts, modelled by any joint distribution. By stating appropriate optimality problems, we show that these results can be used to set the limiting and the retention levels in an optimal way with respect to the probability of joint survival. Alternatively, for fixed retention and limiting levels, the results yield an optimal split of the total premium income between the two parties in the excess of loss contract. This methodology is illustrated numerically on several examples of independent and dependent claim severities. The latter are modelled by a copula function. The effect of varying its dependence parameter and the marginals, on the solutions of the optimality problems and the joint survival probability, has also been explored

Optimal joint survival reinsurance: An efficient frontier approach

The problem of optimal excess of loss reinsurance with a limiting and a retention level is considered. It is demonstrated that this problem can be solved, combining specific risk and performance measures, under some relatively general assumptions for the risk model, under which the premium income is modelled by any non-negative, non-decreasing function, claim arrivals follow a Poisson process and claim amounts are modelled by any continuous joint distribution. As a performance measure, we define the expected profits at time x of the direct insurer and the reinsurer, given their joint survival up to x, and derive explicit expressions for their numerical evaluation. The probability of joint survival of the direct insurer and the reinsurer up to the finite time horizon x is employed as a risk measure. An efficient frontier type approach to setting the limiting and the retention levels, based on the probability of joint survival considered as a risk measure and on the expected profit given joint survival, considered as a performance measure is introduced. Several optimality problems are defined and their solutions are illustrated numerically on several examples of appropriate claim amount distributions, both for the case of dependent and independent claim severitie

Fibromuscular dysplasia of aortic aneurysm vasa vasorum (a rare case report)

Aim. To describe a rare occurrence of fibromuscular vasa vasorum dysplasia of the aortic aneurysm wall.Materials and methods. Surgical material from the ascending aortic aneurysm wall was examined. Longitudinal strips of the aortic wall were excised for histological examination with subsequent 24-h fixation in 10% buffered formalin. A histological isopropanol assay was performed with an automated Logos microwave tissue processor (Milestone, Italy) with subsequent sample embedding into paraffin. Sections were obtained with a rotary microtome (Leica, Germany). Staining was performed with haematoxylin-eosin, van Gieson’s picrofuchsin, orcein for elastic fibres, Hotchkiss’ PAS reaction with alcian blue for glycosaminoglycans. Histological and histochemical properties of the aortic wall were studied and imaged with a Leica DM 1000 microscope (Germany) equipped with a camera ICC50 E at magnifications 40x, 100x, 200x, 400x.Results. The conducted histological examination of the aortic aneurysm wall revealed most pronounced changes in media and adventitia layers. Elastic fibres in media were swollen, homogeneous, crimped, with pronounced dystrophic and necrobiotic changes in smooth myocytes. Regions of compromised cells and elastic fibres in media contained pockets of alcian-positive glycosaminoglycans. Specific changes were revealed in adventitia vasa vasorum in the form of a pronounced wall thickening and lumen narrowing due to dysplastic fibromuscular tissues.Conclusion. A rare form of fibromuscular dysplasia of the vasa vasorum of the ascending aortic aneurysm wall observed in a 43 years-old woman demonstrated the morbid morphology of smooth myocytes, as well as fibrous collagenous and elastic structures. The described features were likely associated with the aortic wall trophic structure and aneurysm morphogenesis