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Ruin probabilities by Padé’s method: simple moments based mixed exponential approximations (Renyi, De Vylder, Cramér-Lundberg), and high precision approximations with both light and heavy tails. (English) Zbl 1422.91323

Summary: We revisit below Padé and other rational approximations for ruin probabilities, of which the approximations mentioned in the title are just particular cases. We provide new simple Tijms-type and moments based approximations, and show that shifted Padé approximations are quite successful even in the case of heavy tailed claims.

MSC:

91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
62P05 Applications of statistics to actuarial sciences and financial mathematics

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