Analysis of a defective renewal equation arising in ruin theory
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Publication:1962817
DOI10.1016/S0167-6687(99)00026-8zbMath1028.91556WikidataQ127207443 ScholiaQ127207443MaRDI QIDQ1962817
X. Sheldon Lin, Gordon E. Willmot
Publication date: 31 January 2000
Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)
failure rateequilibrium distributionstime of ruindeficitmean residual lifetimecompound geometricTijms approximations
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Cites Work
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- A remark on the moments of ruin time in classical risk theory
- The probability and severity of ruin for combinations of exponential claim amount distributions and their translations
- Calculation of the probability of eventual ruin by Beekman's convolution series
- Further use of Shiu's approach to the evaluation of ultimate ruin probabilities
- A probabilistic generalization of Taylor's theorem
- On the distribution of the surplus prior to ruin
- On a class of approximations for ruin and waiting time probabilities
- Exact and approximate properties of the distribution of surplus before and after ruin
- The moments of ruin time in the classical risk model with discrete claim size distribution
- From ruin theory to pricing reset guarantees and perpetual put options
- Refinements and distributional generalizations of Lundberg's inequality
- The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
- Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions
- The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
- Exponential and scale mixtures and equilibrium distributions
- Preservation of certain classes of life distributions under Poisson shock models
- Simplified bounds on the tails of compound distributions
- On the distribution of the duration of negative surplus
- Approximate solutions of severity of ruins
- Tail of compound distributions and excess time
- On the Time Value of Ruin