带扩散扰动的对偶风险模型的门槛分红策略  

The threshold dividend strategy in the dual risk model perturbed by diffusion

作　　者：刘章[1] 明瑞星[2] 王文元[3] 宋秀英[1] 

机构地区：[1]江西农业大学理学院,江西南昌330045 [2]中国科学技术大学统计与金融系,安徽合肥230026 [3]武汉大学数学与统计学院,湖北武汉430072

出　　处：《中国科学技术大学学报》2012年第6期475-481,516,共8页JUSTC

基　　金：江西农业大学青年基金(09003326)资助

摘　　要：研究了一类带干扰(布朗运动)的对偶风险模型,此模型可以用来模拟证券公司的盈余过程(经营收入).利用无穷小分析法,求出了公司在破产前总分红现值期望函数(分红函数)满足的微积分方程组,导出了与该微积分方程组等价的更新方程组.最后,在指数分布收入情形下,我们给出了分红函数在特例下的一般解.The dual risk model perturbed by diffusion （Brownian motion） was studied. The surplus process （operating income） of a securities company could be simulated by this model. Using the infinitesimal analysis, the integro-differential equations of the expected accumulated discounted dividends before bankruptcy were obtained. Then, the renewal equations equivalent to the integro-differential equations were derived. Finally, for exponentially distributed income, the explicit solutions for the expected accumulated discounted dividends were given for special cases.

关 键 词：分红函数 扰动 对偶风险模型 barrier分红策略 threshold分红策略 破产时刻 

分 类 号：O211.5[理学—概率论与数理统计] O211.6[理学—数学]