关于一个离散盈余过程破产概率的上界估计

Estimate on the Upper Bound of Ruin Probability of a Discrete Surplus Process

讨论保险精算研究领域中一种具有随机保费的离散盈余过程破产概率的上界.基于保险公司各度量期保费收入随机波动的现象,将经典的离散泊松盈余过程推广为一种具有随机保费的离散泊松盈余过程.根据关于经典离散泊松盈余过程的Cramer定理,运用随机分析、集合论与数值计算的方法,通过将过程分解成三部分进行估计,在一定的条件下给出与证明了该盈余过程破产概率的一个上界.此项工作可为保险公司优化经营策略提供一定的理论依据.

Study the upper bound of ruin probability of a discrete surplus process with random premium in the research area of insurance actuary.The classical discrete Poisson surplus process is extended as a discrete Poisson surplus process with random premium basing on the fact that premiums obtained of insurance company in various measurement period are random fluctuations.According to the Cramer theorem on the classical discrete Poisson surplus process,using the methods of stochastic analysis,set theory and numerical calculation,through estimating by dividing the process into three parts,an upper bound of ruin probability for the addressed process is proposed and proved under certain conditions.What we do can provide references and suggestions for insurers to optimize their insurance policies.