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On the Gerber–Shiu function for a risk model with multi-layer dividend strategy
Statistics & Probability Letters, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The gerber-shiu expected discounted penalty function for Lévy insurance risk processes
Acta Mathematicae Applicatae Sinica, English Series, 2010A Lévy risk model \(\{X_t\}\) without a Brownian component and with \(\mathbb{E}[X_1] > 0\) is considered, where the upward jumps are bounded by some constant \(-a \geq 0\). The goal is to calculate the Gerber--Shiu expected discounted penalty function \[ \Phi(x) = \mathbb{E}\bigl[ e^{-\delta T} 1_{T < \infty} w(X_{T-},|X_T|) \bigm| X_0 = x\bigr]\;, \]
Zhao, Xiang-Hua, Yin, Chuan-Cun
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Estimating the Gerber–Shiu function by Fourier–Sinc series expansion
Scandinavian Actuarial Journal, 2016In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate.
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Editorial for the special issue on Gerber–Shiu functions
Insurance: Mathematics and Economics, 2010Hansjörg Albrecher +2 more
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Computing the Gerber–Shiu function by frame duality projection
Scandinavian Actuarial Journal, 2019Zhimin Zhang, Wenyuan Wang
exaly
Estimating the Gerber–Shiu function by Fourier–Sinc series expansion
Scandinavian Actuarial Journal, 2017Zhimin Zhang
exaly