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Asymptotics in a time-dependent renewal risk model with stochastic return. (English) Zbl 1230.91076

The paper focuses on a non standard renewal risk model, taking into account the dependence structure between the claim size sequence of an insurance company and the sequence of the inter-arrival times between two claims:
Under the hyphothis that the insurer invests both in risk-free bonds and risky stocks, obtaining a portfolio price depicted by means of a geometric Lévy process, the author frames the model within a stochastic scenario where the claim-size distribution has an extended-regularly-varying tail (ERV). Moreover, a constraint on the Lévy process involving the Laplace exponent is set.
Within this framework, an asymptotic formula for the tail probability of the present value of aggregate claims is provided and the consequence in terms of ruin probability are investigated.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics

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