On the Distribution of the Surplus Prior and at Ruin

DOI10.2143/AST.29.2.504613zbMath1129.62425MaRDI QIDQ5444991

Hanspeter Schmidli

Publication date: 27 February 2008

Published in: ASTIN Bulletin (Search for Journal in Brave)

zbMATH Keywords

Gumbel distributiongeneralized Pareto distributionmaximum domain of attractionCramér conditionRuin, asymptotic distribution, change of measure, Laplace transform, subexponential distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Applications of statistics to actuarial sciences and financial mathematics (62P05)

Related Items (24)

A Note on Gerber–Shiu Functions with an Application ⋮ On asymptotic equivalence among the solutions of some defective renewal equations ⋮ Densities of ruin-related quantities in the Cramér-Lundberg model with Pareto claims ⋮ The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion. ⋮ Ruin probabilities in the Cramér-Lundberg model with temporarily negative capital ⋮ The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. ⋮ On the Gerber-Shiu function and change of measure ⋮ Conditional law of risk processes given that ruin occurs ⋮ Tail bounds for the joint distribution of the surplus prior to and at ruin ⋮ On a Classical Risk Model with a Constant Dividend Barrier ⋮ The Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force ⋮ On the deficit distribution when ruin occurs -- discrete time model ⋮ When does surplus reach a certain level before ruin? ⋮ Über die Verteilung des Überschusses vor und zum Zeitpunkt des Ruins in Semi-Markov-Risikomodellen;On the distribution of the surplus prior to ruin and at ruin in a discrete semi-markov risk model ⋮ Refinements of two-sided bounds for renewal equations ⋮ Asymptotic results for heavy-tailed distributions using defective renewal equations ⋮ Some results on the joint distribution prior to and at the time of ruin in the classical model ⋮ Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model ⋮ The moments of the time of ruin, the surplus before ruin, and the deficit at ruin ⋮ Unnamed Item ⋮ Extended Gerber-Shiu functions in a risk model with interest ⋮ Ruin probabilities and aggregrate claims distributions for shot noise Cox processes ⋮ Loss rates in the single-server queue with complete rejection ⋮ Approximations for moments of deficit at ruin with exponential and subexponential claims.

Cites Work

• Unnamed Item
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• On convolution tails
• Aspects of risk theory
• Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue

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