The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions. [PDF]
Methodol Comput Appl Probab, 2023 AbstractIn this paper, we consider discounted penalty functions, also called Gerber-Shiu functions, in a Markovian shot-noise environment. At first, we exploit the underlying structure of piecewise-deterministic Markov processes (PDMPs) to show that these penalty functions solve certain partial integro-differential equations (PIDEs).
Pojer S, Thonhauser S.
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Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence [PDF]
Risks, 2020 This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times.
Franck Adékambi, Essodina Takouda
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International Journal of Mathematics for Industry, 2023 This paper studies the Gerber–Shiu function for the insurance surplus process with additional investment under the Bachelier model. The Gerber–Shiu function allows us to study the moments of the time of ruin, which is the first time that the surplus is ...
Sutipon Punaluek, Yuri Imamura
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Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion
Mathematics, 2021 In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency.
Wen Su, Yunyun Wang
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Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model
Mathematics, 2020 Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on ...
Wen Su, Wenguang Yu
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Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion
Mathematics, 2023 In this paper, we consider an insurance risk model with two-sided jumps, where downward and upward jumps typically represent claim amounts and random gains, respectively. We use the Laguerre series to expand the Gerber–Shiu function and estimate it based
Kang Hu, Ya Huang, Yingchun Deng
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A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model
Mathematics, 2019 In this paper, we propose a new generalized Gerber−Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time.
Jiechang Ruan +5 more
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Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model [PDF]
Discrete Dynamics in Nature and Society, 2019 This paper studies the statistical estimation of the Gerber-Shiu discounted penalty functions in a general spectrally negative Lévy risk model. Suppose that the claims process and the surplus process can be observed at a sequence of discrete time points.
Yujuan Huang +3 more
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A Note on Gerber–Shiu Function with Delayed Claim Reporting under Constant Force of Interest
Mathematical and Computational Applications, 2022 In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson claim arrival scenario, we derive the differential equation of the Laplace transform of the generalized
Kokou Essiomle, Franck Adekambi
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Fourier-cosine method for Gerber–Shiu functions [PDF]
Insurance: Mathematics and Economics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chau, KW, Yang, H, Yam, SCP
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