马尔可夫环境下聚合索赔的前二阶矩

The First Two Moments of Aggregate Claims in a Markovian Environment

中文关键词:  离散时间保险风险模型  折现聚合索赔  环境过程  矩.

英文关键词:discrete-time insurance risk model  discounted aggregate claims  circumstance process  moment.

中文摘要:

      我们研究了保险风险和金融风险在离散时间马尔可夫环境下折现聚合索赔问题.我们假设索赔额与金融风险岁经济状态波动,经济状态由马尔可夫环境状态描述.在假设下,我们将折现索赔的分布用拉普拉斯变换确定一个微分方程系统,进而,应用微积分方程研究他在马尔可夫环境下的折现聚合索赔的前二阶矩.

英文摘要:

      We consider the discounted aggregate claims when the insurance risks and financial risks are governed by a discrete-time Markovian environment. We assume that the claim sizes and the financial risks fluctuate over time according to the states of economy, which are interpreted as the states of Markovian environment. We will then determine a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under mild assumption. Moreover, using the differentio-integral equation, we will also investigate the first two order moments of discounted aggregate claims in a Markovian environment.