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Refinements and distributional generalizations of Lundberg’s inequality. (English) Zbl 0814.62070
Summary: An upper bound is obtained for the tail of the total claims distribution in terms of a ‘new worse than used’ distribution. A simple bound exists when the claim size distribution is also new worse than used. The classical exponential bound is also refined when the claim size distribution is new worse than used in convex ordering, as well as for other classes of claim size distributions characterized by properties of the failure rate and the mean residual lifetime. Pareto bounds may be used when claim size moments are known. The compound geometric case and ruin probabilities are then considered.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60E15 Inequalities; stochastic orderings
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