In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang（n） risk process （i.e., convolution of n exponential distributions with possibly different parameters） perturbe...In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang（n） risk process （i.e., convolution of n exponential distributions with possibly different parameters） perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.展开更多
The article shows that the situation of agricultural cooperatives in the world in general and agricultural cooperatives in Vietnam in particular are facing certain challenges in the context of globalization in the 21s...The article shows that the situation of agricultural cooperatives in the world in general and agricultural cooperatives in Vietnam in particular are facing certain challenges in the context of globalization in the 21st century.The article points out limitations on:the nature,principles of democratic member control and principles of surplus distribution of the International Cooperative Alliance,as well as Vietnamese law in cooperative management.展开更多
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.展开更多
In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a ...In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.展开更多
In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the ti...In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the time of ruin and derive the integro-differential equations satisfied by these distributions respectively.展开更多
基金Supported by National Natural Science Foundation of China （Grant Nos. 10901164 and 11071037）, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and Natural Science Foundation of CQ CSTC （Grant No. 2009BB8221）
文摘In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang（n） risk process （i.e., convolution of n exponential distributions with possibly different parameters） perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.
文摘The article shows that the situation of agricultural cooperatives in the world in general and agricultural cooperatives in Vietnam in particular are facing certain challenges in the context of globalization in the 21st century.The article points out limitations on:the nature,principles of democratic member control and principles of surplus distribution of the International Cooperative Alliance,as well as Vietnamese law in cooperative management.
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
文摘In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.
基金the National Natural Science Foundation of China (No.19971047).
文摘In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the time of ruin and derive the integro-differential equations satisfied by these distributions respectively.
