带干扰的广义泊松风险模型最优预防策略  

Optimal Prevention Strategy for Generalized Poisson Risk Model with Disturbance

作　　者：周瑾 王传玉[1] 陈哲[1] ZHOU Jin;WANG Chuanyu;CHEN Zhe(School of Mathematics,Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China)

机构地区：[1]安徽工程大学数理与金融学院,安徽芜湖241000

出　　处：《安徽工程大学学报》2022年第2期85-94,共10页Journal of Anhui Polytechnic University

基　　金：安徽省高校自然科学重点研究基金资助项目(KJ2018A0120);安徽工程大学校级科研重点基金资助项目(XJKY08201901)。

摘　　要：文中研究了带干扰的广义泊松风险模型的最优预防策略。在这个模型中,保险人可以投资于一个预防计划,以降低索赔强度,并确定在不确定支出和收入指标下的最优预防策略。同时,用鞅的方法得到破产概率所满足的Lunberg不等式及其确定性公式。证明了在带干扰的广义泊松风险模型最优预防策略中,最优预防量不依赖初始盈余且使得生存概率最大化。最后进行数值模拟,分别考虑扰动和理赔参数对调节系数、生存概率的影响。This paper studies the optimal prevention strategy model of generalized Poisson risk model with disturbance.In this model,the insurer can invest into a prevention plan to reduce claim intensity and determine the optimal prevention strategy under uncertain expenditure and income indicators.At the same time,the inequality and its deterministic formula of ruin probability by martingale method are obtained.In particular,it is proved in the optimal prevention strategy of generalized Poisson risk model with disturbance,the optimal amount of prevention is independent of the initial surplus and the optimal amount of prevention maximizes the survival probability.Finally,numerical simulation is carried out,with the influence of disturbance and claim parameters on adjustment coefficient and survival probability.

关 键 词：干扰 最优预防量 生存概率 鞅方法 

分 类 号：F840.6[经济管理—保险]