On Some alternative estimates of the adjustment coefficient in risk theory

DOI10.1080/03461238.1990.10413878zbMath0755.62076OpenAlexW2152630240MaRDI QIDQ3990299

Paul Deheuvels, Josef G. Steinebach

Publication date: 28 June 1992

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461238.1990.10413878

zbMATH Keywords

convergence ratesorder statisticsconsistencyasymptotic normalitysimulationsrisk processHill estimatoradjustment coefficientprobability of ruinestimation of adjustment coefficientquantile type estimatorstail sum estimators

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Applications of statistics to actuarial sciences and financial mathematics (62P05)

Related Items (6)

Estimating the adjustment coefficient in an ARMA\((p,q)\) risk model ⋮ Limiting behaviour of a geometric-type estimator for tail indices. ⋮ Estimation of the expected discounted penalty function for Lévy insurance risks ⋮ Weak convergence of a bootstrap geometric-type estimator with applications to risk theory ⋮ Review of statistical actuarial risk modelling ⋮ Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model

Cites Work

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• On the estimation of the adjustment coefficient in risk theory via intermediate order statistics
• On asymptotic normality of Hill's estimator for the exponent of regular variation
• A simple general approach to inference about the tail of a distribution
• Empirical bounds for ruin probabilities
• On the estimation of the adjustment coefficient in risk theory by means of stochastic approximation procedures
• Empirical Laplace transform and approximation of compound distributions
• Almost sure convergence of the Hill estimator
• A note on positive supermartingales in ruin theory
• Limit Distributions for Order Statistics. I
• Limit theorems for the ratio of the empirical distribution function to the true distribution function

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