The expected discounted penalty function under a renewal risk model with stochastic income

Zhao, Yongxia; Yin, Chuancun

doi:10.1016/j.amc.2011.11.101

Cited by 17 publications

(21 citation statements)

References 15 publications

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“…By the similar arguments of the Lunderg's fundamental equation in Zhao and Yin [33], we can obtain that equation χ(s) = 0 has exactly two nonnegative roots, denoted as ρ 1 , ρ 2 in this literature. It is clear that…”

Section: Estimation Proceduresmentioning

confidence: 81%

“…By Theorem 3.1 in Zhao and Yin [33], when stochastic premium income follows a compound Poisson process, we known that the expected discounted penalty function satisfies the following renewal equation…”

Section: Remark 1 Letmentioning

confidence: 98%

“…By Lemma 2.1 in Zhao and Yin [33], we known that for δ ≥ 0 and c > 0, the above equation has exactly two nonnegative roots, denoted as ρ 1 , ρ 2 in this literature, and one of the roots ρ 1 equals 0 when δ = 0.…”

Section: The Fourier Transform Of Expected Discounted Penalty Functionmentioning

confidence: 99%

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Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Wang

Huang

et al. 2019

Mathematics

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In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

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Section: Estimation Proceduresmentioning

confidence: 81%

Section: Remark 1 Letmentioning

confidence: 98%

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Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Wang

Huang

et al. 2019

Mathematics

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“…Chau et al [6] used the Fourier-cosine method to evaluate the Gerber-Shiu function. For more studies on Gerber-Shiu function, the interested readers are referred to Yin and Wang [7,8], Asmussen and Albrecher [9], Chi [10], Wang et al [11], Chi and Lin [12], Zhao and Yin [13,14], Shen et al [15], Yu [16][17][18], Yin and Yuen [19,20], Zhao and Yao [21], Zheng et al [22], Huang et al [23], Li et al [24], Zhang et al [25], Yu et al [26], Zeng et al [27,28], Li et al [29], and Dong et al [30].…”

Section: Introductionmentioning

confidence: 99%

Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model

Huang

Pan

et al. 2019

Discrete Dynamics in Nature and Society

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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. Using the observed data, the Gerber-Shiu functions are estimated by the Laguerre series expansion method. Consistent properties are studied under the large sample setting, and simulation results are also presented when the sample size is finite.

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“…It is clear that the Gerber-Shiu discounted penalty function becomes the probability of ruin when δ = 0, W(x, y) = 1. For the recent literature on the Gerber-Shiu discounted penalty function, we can refer to work by Lin et al [1], Zhang et al [2], Yu [3,4], Wang et al [5], Avram et al [6], Zhang [7], Chi [8], Peng and Wang [9], Li et al [10], Huang et al [11], Preischl and Thonhauser [12], Zeng et al [13,14], Yu et al [15], Dickson and Qazvini [16], Zhang and Su [17,18], Li et al [19], and Zhao and Yin [20], among others. In recent years, Gerber-Shiu discounted penalty function has been extended by many actuarial scholars, so that the new risk measures can be used to study more related quantities.…”

Section: Introductionmentioning

confidence: 99%

A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Ruan

Song

et al. 2019

Mathematics

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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. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

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The expected discounted penalty function under a renewal risk model with stochastic income

Cited by 17 publications

References 15 publications

Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model

A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

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