具有相依结构的对偶风险模型的破产概率分析

Analysis of Ruin Probability for the Dual Risk Model with Dependent Structure

摘要: 本文研究了具有相依结构的对偶风险模型，收益金额的分布规则如下：在第i次的收益参考变量大于第i次的收益间隔时间的情形下，下一次的收益额服从第一类概率分布；反之，服从第二类概率分布；并计算了收益间隔时间与收益金额均服从指数分布时的情形，通过求导运算推导得到破产概率的积微分方程，进一步转化为特征方程，通过对比系数法得到了破产概率的显式表达式；最后，为验证模型有效性，选取参数进行了数值模拟。

Abstract: This paper studies the dual risk model with dependent structure, and the distribution rule of the gain amount is as follows: when the i gain reference variable is greater than the i gain inter-arrival time, the next gain amount follows the first-type probability distribution; otherwise, it follows the second-type probability distribution. We calculate the case where both the gain inter-arrival time and the gain amount obey the exponential distribution, derive the integro-differential equation for the ruin probability through differentiation, further transform it into a characteristic equation, and obtain the explicit expression of the ruin probability via the coefficient comparison method. Finally, to verify the validity of the model, we select parameters and carry out numerical simulations.