Refinements and distributional generalizations of Lundberg's inequality

DOI10.1016/0167-6687(94)00019-0zbMath0814.62070OpenAlexW2012018017MaRDI QIDQ1341326

Gordon E. Willmot

Publication date: 9 January 1995

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6687(94)00019-0

zbMATH Keywords

upper boundfailure ratemartingaleMarkov's inequalityconvex orderingruin probabilitiesmean residual lifetimeclaim size distributionsnew worse than used distributionnew worse than used in expectationPareto boundstotal claims distribution

Mathematics Subject Classification ID

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

Related Items (20)

Non-exponential Bounds for Ruin Probability with Interest Effect Included ⋮ Two-Sided Bounds for Ruin Probabilities when the Adjustment Coefficient does not Exist ⋮ The deficit at ruin in the Sparre Andersen model with interest ⋮ Some improvements on the Lundberg bound for the ruin probability ⋮ Bounds on the tails of convolutions of compound distributions ⋮ On the relationship between bounds on the tails of compound distributions ⋮ Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions ⋮ Ruin problems for an autoregressive risk model with dependent rates of interest ⋮ Aging and other distributional properties of discrete compound geometric distributions ⋮ Nonparametric statistical analysis of an upper bound of the ruin probability under large claims ⋮ Analysis of a defective renewal equation arising in ruin theory ⋮ Upper bounds for the tail of the compound negative binomial distribution ⋮ Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison ⋮ Approximation der Ruinwahrscheinlichkeit bei diskreter Zeit mittels eines Resultats von A. Wald ⋮ Non-exponential bounds for stop-loss premiums and ruin probabilities ⋮ Refinements of two-sided bounds for renewal equations ⋮ Aging properties and bounds for ruin probabilities and stop-loss premiums ⋮ An effective method for constructing bounds for ruin probabilities for the surplus process perturbed by diffusion ⋮ Refinements of bounds for tails of compound distributions and ruin probabilities ⋮ Comparison of ruin probability estimates in the presence of heavy tails

Cites Work

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• Error bounds for exponential approximations of geometric convolutions
• On convolution tails
• A property of the generalized inverse Gaussian distribution with some applications
• The NBUC and NWUC classes of life distributions
• Bounds on the delay distribution in GI/G/1 queues
• Use of differential and integral inequalities to bound ruin and queuing probabilities
• Lundberg bounds on the tails of compound distributions
• The total claims distribution under inflationary conditions
• Tail of compound distributions and excess time

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