We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iterati...We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.展开更多
In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive t...In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive the expression of gδ(u) (i.e. the Laplace transform of the first upper exit time). We discuss the expected discounted tax payments for this model and obtain its corresponding integro-differential equations. Finally, for Erlang (2) inter-innovation distribution, closedform expressions for the expected discounted tax payments are given.展开更多
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 paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied b...In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.展开更多
In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then ge...In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.展开更多
Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the di...Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.展开更多
In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy （PCT）. Integro-differential equations （IDE） for its Cerber-Shiu functions and dividend payments function are ...In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy （PCT）. Integro-differential equations （IDE） for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.展开更多
In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new stra...In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.展开更多
文摘We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.
文摘In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive the expression of gδ(u) (i.e. the Laplace transform of the first upper exit time). We discuss the expected discounted tax payments for this model and obtain its corresponding integro-differential equations. Finally, for Erlang (2) inter-innovation distribution, closedform expressions for the expected discounted tax payments are given.
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.
基金supported by the National Natural Science Foundation of China (No. 71801085)。
文摘In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.
基金Supported in part by the National Natural Science Foun-dation of China and the Ministry of Education of China
文摘In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.
基金supported by the Natural Sciences Foundation of China under Grant No.10871064
文摘Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.
基金Supported by the National Basic Research Program of China(973 Program) 2007CB814905the National Natural Science Foundation of China(No.10871102)the Research Fund of the Doctorial Program of Higher Education,the Keygrant Project of Chinese Ministry of Education(No.309009)
文摘In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy （PCT）. Integro-differential equations （IDE） for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.
基金Supported by National Natural Science Foundation of China(Grant No.10871064)Scientific Research Funds of Hu'nan Provincial Education Department(08C883)Hu'nan Provincial Science and Technology Department(2009FJ3141)
文摘In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.
