In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend ...In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.展开更多
在这篇文章中,我们考虑一个最早由Bruno De Finetti提出的问题,风险被描述为带有常利率的古典风险过程。红利按照带常数界的边界策略发放。当盈余量达到常数界时,所有的保费收入不再计入盈余,而是作为红利分发给债券持有人。利用过程的...在这篇文章中,我们考虑一个最早由Bruno De Finetti提出的问题,风险被描述为带有常利率的古典风险过程。红利按照带常数界的边界策略发放。当盈余量达到常数界时,所有的保费收入不再计入盈余,而是作为红利分发给债券持有人。利用过程的马尔可夫性,我们得到了累积期望折现分红函数的显式解。展开更多
Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distr...Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.展开更多
基金The National Natural Science Foundations of China (grant No.10271062 and No.10471076)the Natural Science Foundation of Sandong Province(Y2004A06)the Postdoctoral Research Fund of Qufu Normal University.
基金Supported by the National Natural Science Foundation of China(Nos.71231008,71201173,71301031)Natural Science Foundation of Guangdong Province of China(No.S2012040006838)+1 种基金the High-level Talent Project of Guangdong "Research on Models and Strategies for Optimal Reinsurance,Investment and Dividend"the Post-Doctoral Foundation of China(No.2012M510195)
文摘In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.
基金Supported by the National Natural Science Foundation of China(No.10571167,No.70501028)Beijing Sustentation Fund for Elitist(Grant No.20071D1600800421)National Social Science Foundation of China(Grant No.05&ZD008).
文摘Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.
