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Uniform asymptotics for discounted aggregate claims in dependent risk models. (English) Zbl 1303.91097

The renewal risk model under consideration involves a sequence of identically distributed claim sizes, which are not necessarily independent; the interarrival times are i.i.d. nonnegative random variables. The claim arrival times constitute a renewal counting process.
Within this context, supposing that the insurer can make risk free and risky investments, the price process of the investment portfolio is depicted as a geometric Lévy process.
Under the hypothesis that the claim size distribution belongs to some specific classes of heavy tailed distributions, asymptotic formulae are obtained for the tail probability of discounted aggregate claims and ruin probabilities.

MSC:

91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
60K05 Renewal theory
60G70 Extreme value theory; extremal stochastic processes
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References:

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