带常利率的马氏调节风险模型的期望折现罚金函数的概率解法

The Solution in Probability of the Expected Discounted Penalty Function of a Markov Modulated Risk Model with Constant Interest

研究了带常利率的马氏调节风险模型的期望折现罚金函数.运用概率方法考虑当第n次索赔的发生引起破产时的期望折现罚金函数,以发生第一次索赔为条件进行分析,给出递推公式,进而得到期望折现罚金函数的无穷级数形式,最后给出经典情形下的数值计算结果.

The Markov-modulated risk model with constant interest is considered and the expected discounted penalty function is computed when the ruin is caused by the nth claim by a probability way.By conditioning on the time and the amount of the first claim,the recurrence formula is divived and further the infinite series of the expected discounted penalty function.Finally,numerical illustration for the classical model is given.