The probability and severity of ruin for combinations of exponential claim amount distributions and their translations

DOI10.1016/0167-6687(88)90100-XzbMath0637.62101OpenAlexW2029485082MaRDI QIDQ1098534

François Dufresne, Hans U. Gerber

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0167-6687(88)90100-x

zbMATH Keywords

severity of ruindiscrete time modeltime of ruinprobability of ruincollective risk theorycombination of exponential distributionsclassical compound Poisson model

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Exact distribution theory in statistics (62E15)

Related Items (31)

Ladder height distributions with marks ⋮ VALUING EQUITY-LINKED DEATH BENEFITS IN A REGIME-SWITCHING FRAMEWORK ⋮ The surpluses immediately before and at ruin, and the amount of the claim causing ruin ⋮ Further use of Shiu's approach to the evaluation of ultimate ruin probabilities ⋮ On a risk measure inspired from the ruin probability and the expected deficit at ruin ⋮ Computing the finite-time expected discounted penalty function for a family of Lévy risk processes ⋮ Taylor-series expansion for multivariate characteristics of classical risk processes ⋮ Ruin problems for a discrete time risk model with random interest rate ⋮ A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process ⋮ On the expectations of the present values of the time of ruin perturbed by diffusion. ⋮ On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin ⋮ The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. ⋮ A note on the Taylor series expansions for multivariate characteristics of classical risk processes ⋮ Analysis of a defective renewal equation arising in ruin theory ⋮ Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach ⋮ On two families of bivariate distributions with exponential marginals: aggregation and capital allocation ⋮ The Time Value of Ruin in a Sparre Andersen Model ⋮ The probability of ruin in a discrete semi-Markov risk model ⋮ On the severity of ruin in a Markov-modulated risk model ⋮ On the Distribution of the Deficit at Ruin when Claims are Phase-type ⋮ Valuing equity-linked death benefits in jump diffusion models ⋮ Ruin Probability for the Integrated Gaussian Process with Force of Interest ⋮ On the distribution of surplus immediately after ruin under interest force ⋮ A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk model ⋮ Approximate solutions of severity of ruins ⋮ Exact and approximate properties of the distribution of surplus before and after ruin ⋮ Recursive calculation of the probability and severity of ruin ⋮ Discussion on “On Cramér’s First Contributions to Ruin Theory,” by Ennio Badolati and Sandra Ciccone, Volume 21(2) ⋮ The moments of the time of ruin, the surplus before ruin, and the deficit at ruin ⋮ Optimal prevention of large risks with two types of claims ⋮ Approximations for moments of deficit at ruin with exponential and subexponential claims.

Cites Work

• The probability of ruin for the inverse Gaussian and related processes
• The dilemma between dividends and safety and a generalization of the Lundberg-Cramér formulas
• Unnamed Item
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