Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model

DOI10.1080/03461238.2010.523515zbMath1277.62096OpenAlexW2036826520MaRDI QIDQ2866297

Yasutaka Shimizu

Publication date: 13 December 2013

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

Full work available at URL: https://doi.org/10.1080/03461238.2010.523515

zbMATH Keywords

Laplace transformempirical estimatorexpected discounted penalty functionregularized inversionrisk model perturbed by diffusions

Mathematics Subject Classification ID

Related Items (27)

Saddlepoint approximations to the probability of ruin in finite time for the compound Poisson risk process perturbed by diffusion ⋮ Estimating the Gerber-Shiu function in a Lévy risk model by Laguerre series expansion ⋮ Nonparametric estimation of the expected discounted penalty function in the compound Poisson model ⋮ Estimating the time value of ruin in a Lévy risk model under low-frequency observation ⋮ 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 for a spectrally negative Lévy risk process based on low-frequency observation ⋮ Nonparametric estimation of the finite time ruin probability in the classical risk model ⋮ On a nonparametric estimator for ruin probability in the classical risk model ⋮ Estimating the Gerber–Shiu function by Fourier–Sinc series expansion ⋮ 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 ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ Nonparametric estimation of some dividend problems in the perturbed compound Poisson model ⋮ Unnamed Item ⋮ Statistical estimation for some dividend problems under the compound Poisson risk model ⋮ Unnamed Item ⋮ 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 ⋮ Parametric inference for ruin probability in the classical risk model ⋮ Nonparametric estimation for a spectrally negative Lévy process based on high frequency data ⋮ On a generalization from ruin to default in a Lévy insurance risk model ⋮ 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 ⋮ Estimating the Gerber-Shiu expected discounted penalty function for Lévy risk model ⋮ Review of statistical actuarial risk modelling ⋮ Fourier-Cosine Method for Finite-Time Gerber--Shiu Functions

Cites Work

• Nonparametric renewal function estimation
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• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• On the estimation of the adjustment coefficient in risk theory via intermediate order statistics
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• On the expected discounted penalty function for a perturbed risk process driven by a subordinator
• A new aspect of a risk process and its statistical inference
• Functional estimation for Lévy measures of semimartingales with Poissonian jumps
• Nonparametric estimation of ruin probabilities given a random sample of claims
• A bootstrap procedure for estimating the adjustment coefficients
• Empirical bounds for ruin probabilities
• From ruin theory to pricing reset guarantees and perpetual put options
• Regularized inversion of noisy Laplace transforms
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• A generalized defective renewal equation for the surplus process perturbed by diffusion.
• On Some alternative estimates of the adjustment coefficient in risk theory
• Asymptotic Statistics
• Nonparametric Estimation of the Ruin Probability for Generalized Risk Processes
• Asymptotic properties of power variations of Lévy processes
• Estimation of Dependences Based on Empirical Data
• On the Time Value of Ruin

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