带有利率和贷款的风险模型的负盈余总持续时（英文）  

Total Duration of Negative Surplus for the Risk Model with Credit and Debit Interests

作　　者：何敬民[1] 王冰冰 He Jingmin;Wang Bingbing(College of Science,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]天津理工大学理学院

出　　处：《南开大学学报（自然科学版）》2019年第5期1-8,共8页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by MOE Youth Project of Humanities and Social Sciences(14YJCZH048,15YJCZH204);National Natural Science Foundation of China(11401436,11601382)

摘　　要：研究了带有利率和贷款的风险模型,其中利率是指当保险公司的盈余为正时,公司可以以恒定利率获得一定的利息;而贷款意为当保险公司的盈余为负时,公司可以以恒定的利率向银行借款.通过带有利率与贷款的风险模型的强马尔可夫性,可以得到负盈余总持续时的拉普拉斯变换.更进一步,在索赔服从指数分布的情况下,得到负盈余总持续时的拉普拉斯变换的显性表达式.The risk model with credit and debit interests is investigated, in which credit interest means that the company is allowed to receive credit interest at a constant force of interest while the surplus turns positive, and debit interest means that the insurer can borrow money from the bank at a constant force of interest while the surplus turns negative. By the strong Markov property of the risk model with credit and debit interests, the Laplace-Stieltjes transform for the total duration of negative surplus is obtained. Further, the closed-form expression of the Laplace-Stieltjes transform for the total duration of negative surplus is derived in the case of the exponential distribution.

关 键 词：负盈余的总持续时 拉普拉斯变换 强马尔可夫性 利率 贷款利息 

分 类 号：O211.62[理学—概率论与数理统计] F840[理学—数学]