共查询到19条相似文献,搜索用时 82 毫秒
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建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型.利用全概率公式和泰勒展式,推导出了该模型的Gerber-Shiu函数和绝对破产时刻的累积分红现值期望满足的积分-微分方程及边界条件,借助Volterra方程,给出了Gerber-Shiu函数的解析表达式. 相似文献
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讨论一个任意正整数保费率的复合二项模型.获得了这个模型的Gerber-Shiu 罚金函数值满足的线性方程、一个上界、一个下界. 相似文献
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本文考虑变保费风险模型,假设保费率是随时间变化的,研究了其Gerber-Shiu惩罚函数.通过无穷小方法给出 Gerber-Shiu惩罚函数所满足的积分一微分方程;在指数索赔下,给出其破产时赤字的数学期望及破产时的拉普拉斯变换. 相似文献
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在经典复合泊松模型的基础上,研究线性红利边界下两步保费率风险模型的Gerber-Shiu贴现罚金函数.根本目的是推导出它的微积分方程和偏微积分方程.同时给出了线性红利边界下Lundberg基本方程;利用Laplace变换求出了最终破产概率. 相似文献
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该文考虑了常数障碍分红策略下的Erlang(2)模型,研究了Gerber-Shiu折现罚金函数和期望折现分红,导出了它们所满足的积分微分方程,并分析了它们的解. 相似文献
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《数学的实践与认识》2017,(17)
提出了一种保费收取过程为二项过程而索赔过程为其稀疏过程的风险模型,讨论了该模型的Gerber-Shiu折现罚金函数,得到了Gerber-Shiu折现罚金函数所满足的更新方程和渐近估计式,并且根据Gerber-Shiu折现罚金函数的特点,还得到了一些相关精算量的渐近估计式. 相似文献
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在常利率环境下,研究当索赔时间间隔为Erlang(2)分布且保费收取为两步保费的风险模型,推导出该模型Gerber-Shiu罚金折现期望函数所满足的微积分方程. 相似文献
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高珊 《纯粹数学与应用数学》2009,25(2):251-257
给出了具有边界红利策略的Erlang(2)风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以低于保费率的常速率予以支付.对于该模型,本文推导了Gerber-Shiu折现惩罚函数所满足的两个积分-微分方程和更新方程. 相似文献
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In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, respectively. When the surplus is above this threshold level, dividends are paid at a constant rate that does not exceed the premium rate. Two systems of integro-differential equations for discounted penalty functions are derived, based on whether the surplus is above this threshold level. Laplace transformations of the discounted penalty functions when the surplus is below the threshold level are obtained. And we also derive a system of renewal equations satisfied by the discounted penalty function with initial surplus above the threshold strategy via the Dickson-Hipp operator. Finally, analytical solutions of the two systems of integro-differential equations are presented. 相似文献
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在常数红利策略下考虑索赔时间间隔为指数分布与Erlang(2)分布混合时的风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以等于保费率的常速率予以支付.对于此风险模型,推导并求解了罚金折现期望函数所满足的微积分方程,并在索赔量为指数分布时研究了其解的形式. 相似文献
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In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided. 相似文献
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In this paper, the risk model under constant dividend
barrier strategy is studied, in which the premium income follows a compound
Poisson process and the arrival of the claims is a p-thinning process of the
premium arrival process. The integral equations with boundary conditions for
the expected discounted aggregate dividend payments and the expected discounted
penalty function until ruin are derived. In addition, the explicit expressions
for the Laplace transform of the ruin time and the expected aggregate discounted
dividend payments until ruin are given when the individual stochastic premium
amount and claim amount are exponentially distributed. Finally, the optimal
barrier is presented under the condition of maximizing the expectation of the
difference between discounted aggregate dividends until ruin and the deficit at ruin. 相似文献
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This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given. 相似文献
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This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given. 相似文献