Asymptotic estimates of insurance tarifs in the individual risk model
The individual risk model is a model of insurance in which an insurance portfolio, i.e., the set of insurance contracts concluded simultaneously or during a rather short interval of time is considered; the insurance premiums are assembled during the formation of the insurance portfolio, and insurance events (accidents) may occur while the insurance contracts are valid, which result in insurance pay-offs (claims). One of the important problems that may be set within the framework of this model is the estimation of the insurance tariffs (premiums) ensuring given (usually close to 1) probability of the insurer's ``nonruin.'' In the present article, asymptotic estimates of tariffs that are least admissible for the insurer are obtained for the individual risk model under the conditions that an insurance premium and an insurance indemnity (claim) for each contract of the insurance portfolio are dependent random variables. The least admissible insurance tariffs are determined so that they provide the given lower bound of ``nonruin'' probability, i.e., probability that the sum of insurance portfolio claims will not exceed the sum of all insurance premiums included in the insurance fund and the initial capital related to the given portfolio.
scientific article; zbMATH DE number 1213228
scientific article