Abstract
In an insurance company, the risk process estimation and the estimation of the ruin probability are important concerns for an actuary: for researchers, at the theoretical level, and for the management of the company, as these influence the insurer strategy. We consider the evolution over an extended period of time of an insurer surplus process. In this paper, we present some methods for the evaluation of the ruin probability and the reserve fund. We discuss the ruin probability with respect to the parameters of the individual claim distribution, the load factor of premiums, and the intensity parameter of the number of claims process. We analyse the model for which the premiums are computed based on the mean value principle. Also, we attempt the case when the initial capital is proportional to the value of the mean individual claim. We give numerical illustration.
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