摘要
考虑保费率交替变化的马氏调制风险模型,首先研究保费率变化为两状态平稳遍历马氏过程下该模型的生存概率,并推导出具有平稳初始状态分布的生存概率满足的积分-微分方程;然后通过Laplace变换对该方程的解进行了研究,利用方程组系数矩阵的非负特征根,得到了初始资本为零时生存概率的精确表达式.最后作为特例,研究了索赔额为指数分布下生存概率的具体表达形式.
This paper considers a Markov-modulated risk model with alternative premium rate. Firstly, when the premium rate is controlled by a steady and traversal Markov process in the two-states case, it analyzes survival probabilities for the model and gives integro-differential equations for the survival probabilities based on a stationary initial distribution. Then it fully discusses the solutions of the integro-differential equations with Laplace transforms, and ultilzing the non-negative root of the characteristic equation of coefficient matrix, the exact formulae for survival probabilities are obtained when the initial surplus is zero. At last, the concrete survival probabilities are derived for the exponential claim size distributions.
出处
《系统工程学报》
CSCD
北大核心
2011年第6期752-759,共8页
Journal of Systems Engineering
基金
甘肃省自然科学基金资助项目(0809RJZA019)
甘肃省高校研究生导师科研基金资助项目(0703-10)
关键词
马氏过程
生存概率
积分-微分方程
LAPLACE变换
特征方程
Markov process
survival probability
integro-differential equation
Laplace transform
characteristic equation
