Approximations for moments of deficit at ruin with exponential and subexponential claims.

DOI10.1016/S0167-7152(02)00234-1zbMath1092.62599OpenAlexW2145411551MaRDI QIDQ1871297

Hailiang Yang, Qi-he Tang, Ye Bin Cheng

Publication date: 7 May 2003

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(02)00234-1

zbMATH Keywords

AsymptoticsmodelRuin probabilities\(\phi\)-momentsAscending ladderRenewal riskThe class \(\mathcal S(\gamma)\)

Mathematics Subject Classification ID

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

Related Items (9)

\(\mathrm{G}/\mathrm{M}/1\) type structure of a risk model with general claim sizes in a Markovian environment ⋮ Asymptotics for the moments of the overshoot and undershoot of a random walk ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ On asymptotics of deficit distribution and its moments at the time of ruin ⋮ Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process ⋮ The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments ⋮ The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model ⋮ The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments ⋮ On domination problem of non-negative distributions

Cites Work

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• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• The probability and severity of ruin for combinations of exponential claim amount distributions and their translations
• The surpluses immediately before and at ruin, and the amount of the claim causing ruin
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• Subexponential distributions and characterizations of related classes
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
• Two-sided bounds of ruin probabilities
• On the Distribution of the Surplus Prior and at Ruin
• The Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force

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