Densities of ruin-related quantities in the Cramér-Lundberg model with Pareto claims

DOI10.1007/s11009-017-9551-xzbMath1407.91136OpenAlexW2590295689MaRDI QIDQ1703030

Danijel Grahovac

Publication date: 1 March 2018

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-017-9551-x

zbMATH Keywords

heavy-tailed distributionsscale functionPareto distributionCramér-Lundberg modelruin-related quantities

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Applications of statistics to actuarial sciences and financial mathematics (62P05) Statistics of extreme values; tail inference (62G32)

Related Items

Relations between integrated tails and moments based on the deficit at ruin in the renewal risk model, Unnamed Item, TheW,Zscale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems, Functional sensitivity analysis of ruin probability in the classical risk models

Uses Software

• Mathematica

Cites Work

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• Gerber-Shiu risk theory
• On ruin probability and aggregate claim representations for Pareto claim size distributions
• A note on scale functions and the time value of ruin for Lévy insurance risk processes
• On a generalization of the Gerber-Shiu function to path-dependent penalties
• On the Laplace transform of the Pareto distribution
• On the distribution of the surplus prior to ruin
• Exact and approximate properties of the distribution of surplus before and after ruin
• On some measures of the severity of ruin in the classical Poisson model
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• A solution to the ruin problem for Pareto distributions.
• Ruin probabilities and overshoots for general Lévy insurance risk processes
• Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory
• Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases
• Exact waiting time and queue size distributions for equilibrium \(M/G/1\) queues with Pareto service
• Introductory lectures on fluctuations of Lévy processes with applications.
• The Theory of Scale Functions for Spectrally Negative Lévy Processes
• On extreme ruinous behaviour of Lévy insurance risk processes
• Approximations to ruin probability in the presence of an upper absorbing barrier
• On the Distribution of the Surplus Prior and at Ruin
• On the Time Value of Ruin