In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is E...In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.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
We consider the Sparre Andersen model modified by the inclusion of interest on the surplus. Approximation for the ultimate ruin probability is derived by rounding. And upper bound and lower bound are also derived by r...We consider the Sparre Andersen model modified by the inclusion of interest on the surplus. Approximation for the ultimate ruin probability is derived by rounding. And upper bound and lower bound are also derived by rounding-down and rounding-up respectively. According to the upper bound and lower bound, we can easily obtain the error estimation of the approximation. Applications of the results to the compound Poisson model are given.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
基金Supported by the NNSF of China(10471076)the NSF of Shandong Province(Y2004A06)the Key Project of the Ministry of Education of China(206091).
文摘In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.
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 by the National Natural Science Foundation of China(No.10571051)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20040542006).
文摘We consider the Sparre Andersen model modified by the inclusion of interest on the surplus. Approximation for the ultimate ruin probability is derived by rounding. And upper bound and lower bound are also derived by rounding-down and rounding-up respectively. According to the upper bound and lower bound, we can easily obtain the error estimation of the approximation. Applications of the results to the compound Poisson model are given.
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.
