摘要
考虑一类带扰动的相依风险模型,其中,扰动项由布朗运动刻画,索赔间隔时间服从Erlang(n)分布,索赔额的条件密度为两个概率密度的混合.针对此类风险过程,以Gerber-Shiu惩罚函数为研究对象,首先得到了由索赔导致破产和扰动导致破产两种情况下惩罚函数满足的积分-微分方程以及拉普拉斯变换的表达式,然后根据广义Lundberg方程根求出惩罚函数满足的瑕疵更新方程.
We consider a class of risk process with dependent structure and perturbation,in which the perturbed term is driven by Brownian motion,the interclaim times follow Erlang(n)distribution and the conditional density of the claim sizes is a mixture of two probability densities.The goal of this paper is to study the Gerber-Shiu functions when ruin is due to claims and oscillations respectively.We derive some integro-differential equations and the Laplace transforms for the expected discounted penalty functions,Then,by using the roots of the generalized Lundberg equation,we show that the expected penalty functions satisfy some certain defective renewal equations.
作者
包振华
李彩玲
BAO Zhenhua;LI Cailing(School of Mathematics,Liaoning Normal University,Dalian 116081,China)
出处
《辽宁师范大学学报（自然科学版）》
CAS
2024年第4期433-440,共8页
Journal of Liaoning Normal University:Natural Science Edition
基金
辽宁省教育厅基本科研项目(JYTMS20231043)。
