On the estimation of the adjustment coefficient in risk theory via intermediate order statistics

DOI10.1016/0167-6687(91)90022-PzbMath0732.62100OpenAlexW2110026204MaRDI QIDQ808605

Miklós Csörgő, Josef G. Steinebach

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1016/0167-6687(91)90022-p

zbMATH Keywords

rates of convergenceruin probabilitylight trafficstrong consistencyrisk theoryqueueing modelslaws of iterated logarithmsimulation studiesbusy cyclesestimation of adjustment coefficientsmaximum waiting timessequence of intermediate order statistics

Mathematics Subject Classification ID

Related Items (14)

Estimation of the Lundberg coefficient for a Markov modulated risk model ⋮ On Some alternative estimates of the adjustment coefficient in risk theory ⋮ Estimating the adjustment coefficient in an ARMA\((p,q)\) risk model ⋮ Limiting behaviour of a geometric-type estimator for tail indices. ⋮ A bootstrap procedure for estimating the adjustment coefficients ⋮ On the deficit distribution when ruin occurs -- discrete time model ⋮ Estimation of the expected discounted penalty function for Lévy insurance risks ⋮ Empirical likelihood method for intermediate quantiles ⋮ Edgeworth expansion for an estimator of the adjustment coefficient ⋮ Weak convergence of a bootstrap geometric-type estimator with applications to risk theory ⋮ Review of statistical actuarial risk modelling ⋮ Monitoring risk in a ruin model perturbed by diffusion ⋮ Jackknife method for intermediate quantiles ⋮ Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model

Cites Work

• Extremes and related properties of random sequences and processes
• Limiting multivariate distributions of intermediate order statistics
• A note on the adjustment coefficient in ruin theory
• Strong laws for the k-th order statistic when k\(\leq c\,\log _ 2\,n\)
• Estimates for the probability of ruin starting with a large initial reserve
• On the tail behaviour of quantile processes
• Approximation of intermediate quantile processes
• On the estimation of the adjustment coefficient in risk theory by means of stochastic approximation procedures
• Empirical Laplace transform and approximation of compound distributions
• A note on positive supermartingales in ruin theory
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