带相依结构和常值红利界限风险模型的Gerber-Shiu贴现惩罚函数
The Gerber-Shiu Discounted Penalty Function for the Risk Model with Dependence Structure and a Constant Dividend Barrier
摘要: 我们考虑的是带相依结构和常值红利界限的复合泊松风险模型，其中索赔时间和索赔额服从某种二元分布。我们可以导出Gerber-Shiu贴现惩罚函数的微积分方程，我们还求解了该微积分方程，证明其解是无界限条件下的Gerber-Shiu函数和相关齐次微积分线性方程解的组合。
Abstract: We consider a compound Poisson risk model with dependence and a constant dividend barrier, where the claim amount and the interclaim time follow some bivariate distribution. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.
文章引用：郭红爽. 带相依结构和常值红利界限风险模型的Gerber-Shiu贴现惩罚函数[J]. 理论数学, 2024, 14(5): 60-68. https://doi.org/10.12677/pm.2024.145161

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