Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

Yu, Wenguang

doi:10.1155/2013/579534

Cited by 9 publications

(6 citation statements)

References 18 publications

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“…The barrier strategy was initially proposed by De Finetti [13] for a binomial model. From then on, barrier strategies have been studied in a number of papers and books, including Lin et al [14], Dickson and Waters [15], Li and Lu [16], Yu [17][18][19], Yao et al [20], Zhu [21], Tan et al [22], and references therein for details. The purpose of this paper is to extend some results in Li and Garrido [5] and Yang and Zhang [9].…”

Section: The Risk Modelmentioning

confidence: 99%

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

Huang

2014

Mathematical Problems in Engineering

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This paper constructs a Sparre Andersen risk model with a constant dividend barrier in which the claim interarrival distribution is a mixture of an exponential distribution and an Erlang(n) distribution. We derive the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function of this risk model. Finally, we provide a numerical example. The Risk ModelConsider a Sparre Andersen risk model,where ≥ 0 represents the initial capital, is the insurer's rate of premium income per unit time, and { ( ), ≥ 0} is the claim number process representing the number of claims up to time . { , ≥ 1} is a sequence of i.i.d. random variables representing the individual claim amounts with distribution function ( ) and density function ( ) with mean . We assume that { ( ), ≥ 0} and { , ≥ 1} are independent. Let { , ≥ 1} be sequence i.i.d. random variables, which represent the claim interarrival times, and has a density function ( ),where ≥ 1 is a positive integer, ≥ 0, 1 , 2 ≥ 0, and 1 + 2 = 1. We further assume that [ ] > [ ] for all , which ensure that lim → ∞ ( ) = ∞ almost surely. Throughout the paper we use the convention that ∑ 0 =1 = 0. In recent years the Sparre Andersen model has been studied extensively. Ruin probabilities and many ruin related quantities such as the marginal and joint defective distributions of the time to ruin, the deficit at ruin, the surplus prior to ruin, and the claim size causing ruin have received considerable attention. Some related results can be found in Cai and Dickson [1], Sun and Yang [2], Gerber and Shiu [3], and Ko [4]. Li and Garrido [5] consider a compound renewal (Sparre Andersen) risk process in the presence of a constant dividend barrier in which the claim waiting times are generalized Erlang(n) distributed. The Sparre Andersen model with phase-type interclaim times has been studied by Ren [6]. Ng and Yang [7] study the ruin probability and the distribution of the severity of ruin in risk models with phasetype claims. Landriault and Willmot [8] study the Gerber-Shiu function in a Sparre Andersen model with general interclaim times. Yang and Zhang [9] study a Sparre Andersen model in which the interclaim times are generalized Erlang(n) distributed. They assume that the premium rate is a step function depending on the current surplus level. Landriault and Sendova [10] generalize the Sparre Andersen dual risk model with Erlang(n) interinnovation times by adding a budget-restriction strategy. Shi and Landriault [11] utilize the multivariate version of Lagrange expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely, the combination of exponentials. Yang and Sendova [12] study the Sparre Andersen dual risk model in which the times

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Section: The Risk Modelmentioning

confidence: 99%

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

Huang

2014

Mathematical Problems in Engineering

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“…The classical risk model and extended risk models, such as those with dividend, investment or capital injection strategy, all require insurance companies to continuously observe the reserve process, which will greatly increase the operating costs of insurance companies. Relevant literature can be consulted Chi and Lin [1], Yin et al [2], Li and Lu [3], Zeng et al [4,5], Yu et al [6], Zhou et al [7], Yu [8], Zhang et al [9], Zhou et al [10], Yu et al [11], Xu et al [12], Liu et al [13], Peng and Wang [14], Wang et al [15]. In order to reduce operating costs, insurance companies usually choose to observe reserve process regularly.…”

Section: Introductionmentioning

confidence: 99%

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Guo

Wang

et al. 2020

Mathematics

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In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

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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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Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

Cited by 9 publications

References 18 publications

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

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

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