On a nonparametric estimator for ruin probability in the classical risk model

DOI10.1080/03461238.2012.691427zbMath1401.91217OpenAlexW2068140740MaRDI QIDQ4576854

Hailiang Yang, Hu Yang, Zhimin Zhang

Publication date: 11 July 2018

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

Full work available at URL: http://hdl.handle.net/10722/198105

zbMATH Keywords

Fourier transformasymptotic normalityvariancebiaskernelruin probability

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Nonparametric estimation (62G05)

Related Items (24)

Estimating the Gerber-Shiu function in a Lévy risk model by Laguerre series expansion ⋮ Estimating the time value of ruin in a Lévy risk model under low-frequency observation ⋮ Nonparametric estimation of the claim amount in the strong stability analysis of the classical risk model ⋮ Estimating Gerber-Shiu functions from discretely observed Lévy driven surplus ⋮ Estimating the Gerber-Shiu function under a risk model with stochastic income by Laguerre series expansion ⋮ Nonparametric estimation of the finite time ruin probability in the classical risk model ⋮ Estimating the Gerber–Shiu function by Fourier–Sinc series expansion ⋮ Sensitivity of the stability bound for ruin probabilities to claim distributions ⋮ Nonparametric estimation of ruin probability by complex Fourier series expansion in the compound Poisson model ⋮ A new efficient method for estimating the Gerber–Shiu function in the classical risk model ⋮ Threshold estimation for a spectrally negative Lévy process ⋮ A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model ⋮ Statistical estimation for some dividend problems under the compound Poisson risk model ⋮ Nonparametric estimate of the ruin probability in a pure-jump Lévy risk model ⋮ Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion ⋮ Approximation of the ruin probability using the scaled Laplace transform inversion ⋮ Nonparametric estimation for a spectrally negative Lévy process based on high frequency data ⋮ A Fourier-cosine method for finite-time ruin probabilities ⋮ Nonparametric estimation for the ruin probability in a Lévy risk model under low-frequency observation ⋮ Estimating the Gerber-Shiu function in the perturbed compound Poisson model by Laguerre series expansion ⋮ Interval estimation of the ruin probability in the classical compound Poisson risk model ⋮ Estimating the Gerber-Shiu expected discounted penalty function for Lévy risk model ⋮ Estimating the Gerber-Shiu function in a compound Poisson risk model with stochastic premium income ⋮ Functional sensitivity analysis of ruin probability in the classical risk models

Uses Software

• KernSmooth

Cites Work

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• On ruin probability and aggregate claim representations for Pareto claim size distributions
• Nonparametric estimators for the probability of ruin
• Nonparametric estimation of ruin probabilities given a random sample of claims
• Mean integrated squared error of kernel estimators when the density and its derivative are not necessarily continuous
• Empirical bounds for ruin probabilities
• A solution to the ruin problem for Pareto distributions.
• Nonparametric estimation of compound distributions with applications in insurance
• Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model
• Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday
• Semiparametric Estimation for Non-Ruin Probabilities
• Introduction to nonparametric estimation

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