随机利率下相依索赔的离散风险模型的分红问题  

The Dividend Problems in the Correlated Discrete Risk Model under Stochastic Interest Rates

作　　者：彭丹[1,2] 侯振挺[1] 刘再明[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075 [2]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《应用数学学报》2011年第6期1056-1067,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11071258);教育部人文社会科学青年基金(10YJC630144)资助项目

摘　　要：本文考虑随机利率下相依索赔的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生,当资产盈余达到边界b时,公司给投保者分发一定红利;考虑预期红利的现值时,假设利率服从一有限状态空间的马尔可夫链,我们得到了破产前预期累积分红所满足的差分方程及特殊索赔情形下预期累积分红现值的精确解析式,并结合实例进行了数值模拟.This paper studies a correlated discrete risk model under stochastic interest rates, in which every main claim may produce a by-claim and the occurrence of the byclaim may be delayed. The company pays dividends to policyholders when the surplus is higher than a constant dividend barrier b. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space, we have obtained the difference equations for the expected present value of total dividend payments prior to ruin. Explicit expressions for the corresponding results are derived in a special case, numerical examples are also given.

关 键 词：红利 相依索赔 随机利率 离散风险模型 

分 类 号：O211.67[理学—概率论与数理统计]