This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with gi...This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.展开更多
A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a dis...A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.展开更多
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 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, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend pa...In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.展开更多
We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of divid...We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved.Furthermore,we derive an integro-differential equation for the moment generating function,through which we analyze the higher moment of the present value of dividend payments.Finally,closed-form expressions for exponential claims are given.展开更多
The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the ab...The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.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
基金supported in part by Hubei Normal University Post-graduate Foundation(2007D59 and 2007D60)the Science and Technology foundation of Hubei(D20092207)the National Natural Science Foundation of China(10671149)
文摘This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.
基金Supported by the NNSF of China(10471076)the Science Foundation of Qufu Normal University.
文摘A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.
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.
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 Natural Science Foundation of China (10971157)the Fundamental Research Funds for the Central Universities
文摘In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.
文摘We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved.Furthermore,we derive an integro-differential equation for the moment generating function,through which we analyze the higher moment of the present value of dividend payments.Finally,closed-form expressions for exponential claims are given.
基金Supported by the National Natural Science Foundation of China(11701319,11571198).
文摘The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.
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.
基金supported by Anhui Province Youth Foundation(2009SQRZ166)National Natural Science Foundation of China(10971068)+1 种基金National Basic Research Program of China(973 Program)(2007CB814904)Program for New Century Excellent Talents in University(NCET-09-0356)
