Risk processes with delayed claims for heavy tailed distributions


We study the ruin problem for a non-life insurance company, whose risk process has the following features: claims are not immediately settled, heavy tailed claims distributions. We prove a large deviation principle for the total claim amount process, and then we provide an asymptotic estimates for the logarithm of the in nite horizon ruin probabilities.

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Keywords: Ruin probabilities; Shot noise process; Semiexponential distributions; Large deviations

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