Ruin Probability Based on a Generalized Erlang(2) Distribution and Stochastic Income Risk Model

在本研究中，我们构建了一个包含随机收入的风险模型。在此模型中，索赔间隔时间假定遵循广义Erlang(2)分布，同时保费收入假定服从指数分布。通过数学推导，我们获得了破产概率的拉普拉斯变换以及瑕疵更新方程。此外，在索赔额服从指数分布的条件下，我们推导出了破产概率的显示表达式。In this study, we construct a risk model incorporating stochastic income. In this model, the claim inter-arrival times are assumed to follow a generalized Erlang(2) distribution, while the premium income is assumed to follow an exponential distribution. Through mathematical derivation, we obtain the Laplace transform of the ruin probability as well as a defective renewal equation. Furthermore, under the condition that claim sizes follow an exponential distribution, we derive an explicit expression for the ruin probability.