摘要
在引入投资的情况下,对经典离散时间风险模型的保费收取、索赔过程及险种三个方面进行推广。引入双险种,且保险收取与索赔过程服从二项分布,利用等价变换及全概率公式得到模型的破产概率积分表达式,通过鞅方法证明改进后的模型存在破产概率上界,并应用停时定理证明该破产概率上界优于不带投资情况下的破产概率上界。
In the improvement of the premium collection, claim procedures, and insurance types of the classical discrete risk model, a double-type insurance was introduced whose premium collection and claim procedures satisfied the binomial distribution under the circumstances of investment.Then, the integral expression of the ruin probability was derived by using the methods of mathematical deduction including equivalent transformation and total probability formula. Finally, with the method of martingale, the upper bound of the ruin probability of the improved model was derived, which was later proved superior to that of classical discrete risk model without investment by using the method of stopping time theorem.
作者
王素素
周绍伟
WANG Susu;ZHOU Shaowei(College of Mathematics and Systems Science,Shandong University of Science andTechnology,Qingdao,Shandong 266590,China)
出处
《山东科技大学学报（自然科学版）》
CAS
北大核心
2018年第6期49-54,92,共7页
Journal of Shandong University of Science and Technology(Natural Science)
基金
山东省优秀中青年科学家科研奖励基金项目(BS2014SF005)
山东省统计科研重点课题(KT15105)
关键词
离散风险模型
破产概率
马尔科夫利率
鞅
discrete risk model
ruin probability
Markov chain interest
martingale
作者简介
王素素（1993-），女，山东东营人，硕士研究生，主要从事保险精算的研究.;周绍伟（1979-），女，山东泰安人，副教授，博士，主要从事随机控制、风险理论的研究，本文通信作者.E-mail：1914532073@qq.com
