In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability fun...In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.展开更多
In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generaliz...In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.展开更多
In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are pai...In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.展开更多
Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and com...Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.展开更多
This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid ...This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend.In this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived.When the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained.Finally,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.展开更多
We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting r...We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.展开更多
We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same wa...We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.展开更多
目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的...目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。展开更多
基金Supported in part by the National Natural Science Foundation of China, the Guangdong Natural Science Foundation (S2011010004511)the Fundamental Research Funds for the Central Universities of China (201120102020005)
文摘In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.
文摘In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.
文摘In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.
文摘Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.
基金supported by the National Natural Science Foundation of China under Grant No.11371321the Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)
文摘This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend.In this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived.When the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained.Finally,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.
基金The author is grateful to the referees for their comments and suggestions. This work was supported by the National Natural Science Foundation of China and the Ministry of Education of China.
文摘We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.
基金Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China
文摘We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.
文摘目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。
