李学锋,郭仲凯.常利率下带干扰的复合 Poisson-Geometric风险模型的期望折现罚金函数[J].中南民族大学学报自然科学版,2018,(4):157-160
常利率下带干扰的复合 Poisson-Geometric风险模型的期望折现罚金函数
The Expected Discounted Penalty Function for a Compound Poisson-Geometric Risk Model with Constant Interest and Disturbance
  
DOI:10.12130/znmdzk.20180431
中文关键词: 复合 Poisson-Geometric 风险模型  破产概率  期望折现罚金函数  积分-微分方程
英文关键词: compound Poisson-Geometric risk model  ruin probability  expected discounted penalty function  integrodifferential equation
基金项目:国家自然科学基金资助项目(11801575) ; 中央高校基本科研业务专项资金资助项目(CZQ14022)
作者单位
李学锋,郭仲凯 中南民族大学 数学与统计学学院武汉 430076 
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中文摘要:
      考虑一类常利率下带随机干扰的风险模型, 其中保费收取为时间 t 的线性函数而索赔过程为复合Poisson-Geometric 过程. 利用盈余过程的强马氏性、全期望公式及Ito 积分公式得到期望折现罚金函数的积分-微分方程,进一步得到破产概率的积分-微分方程及其在索赔为指数分布情形下的特殊形式, 同时还得出破产时赤字的概率分布.
英文摘要:
      In this paper, a compound Poisson-Geometric risk model with constant interest and disturbance is considered. In the model, the premium income is a linear function of time t and the process of the claims follow compound PoissonGeometric process. By the strong Markov property of the surplus process,the total expectation formula and the Ito formula,the integro-differential equation of the model for the expected discounted penalty function is derived. Furthermore, the integro-differential equation for the ruin probability is obtained. When the claims are exponentially distributed, the special form of the integro-differential equation for the ruin probability is provided. At the same time, the distribution of the deficit at ruin is also obtained.
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