%0 Journal Article
%T 基于广义Erlang(2)分布和随机收入风险模型的破产概率<br>Ruin Probability Based on a Generalized Erlang(2) Distribution and Stochastic Income Risk Model
%A 徐文娟
%J Advances in Applied Mathematics
%P 198-212
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.146312
%X 在本研究中&#65292;我们构建了一个包含随机收入的风险模型。在此模型中&#65292;索赔间隔时间假定遵循广义Erlang(2)分布&#65292;同时保费收入假定服从指数分布。通过数学推导&#65292;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&#65292;在索赔额服从指数分布的条件下&#65292;我们推导出了破产概率的显示表达式。<br>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.
%K 破产概率&#65292
%K 指数分布&#65292
%K 广义Erlang(2)分布&#65292
%K 拉普拉斯变换<br>Probability of Bankruptcy
%K Exponential Distribution
%K Generalized Erlang(2) Distribution
%K Laplace Transform
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=117588