Because of regulation projects from control organizations such as the European solvency II reform and recent economic events, insurance companies need to consolidate their capital reserve with coherent amounts allocated to the whole company and to each line of business. The present study considers an insurance portfolio consisting of several lines of risk which are linked by a copula and aims to evaluate not only the capital allocation for the overall portfolio but also the contribution of each risk over their aggregation. We use the tail value at risk (TVaR) as risk measure. The handy form of the FGM copula permits an exact expression for the TVaR of the sum of the risks and for the TVaR-based allocations when claim amounts are exponentially distributed and distributed as a mixture of exponentials. We first examine the bivariate model and then the multivariate case. We also show how to approximate the TVaR of the aggregate risk and the contribution of each risk when using any copula.

The LCOT is a self-administered test designed to assess olfactory deficits. Altogether, 525 subjects contributed to the validation. Elderly participants were well represented in this sample. In a validation study (study 1), 407 healthy and 17 anosmic volunteers between 15 and 91 years of age underwent threshold, supraliminal detection, and identification testing. Cutoff values for normosmia and hyposmia were calculated and applied in a second study in a group of patients with smell complaints and in a group of Alzheimer patients with age-matched controls. Incidence of smell deficit was estimated at 5.6% in the healthy population of study 1, and at 16% in the elderly control group of study 2. Assessment of the ability of each subtest to discriminate between groups showed that LCOT is relevant to differentiating between perception and identification deficits and between Alzheimer's and hyposmic patients.