复合二项风险模型和双险种风险模型的进一步研究概率论与数理统计专业论文.docxVIP

山东科技大学硕士学位论文摘要 山东科技大学硕士学位论文 摘要 摘 要 经典风险模型是最基本的风险模型，但这类模型在某些实际问题的应用上具有一定 的局限性。本文在经典风险模型的基础上，从不同的方面对其进行推广得到了几个新的 风险模型，并对这些模型进行了深入的研究： (1)考虑到保险公司退保事件的发生，将普通复合二项风险模型推广为带退保的复 合二项风险模型，得到了此模型的破产概率及其 Lundberg 上界。 (2)在保单到达过程和理赔到达过程相关的条件下，考虑到利率与干扰因素，建立 了带投资和干扰的更贴近现实的复合二项风险模型，用鞅方法得到了此模型破产概率及 其 Lundberg 上界。 (3)考虑投资收益的情况下，对具有混合保费收入的双险种复合二项风险模型进行 扩展，建立一个带投资的保费随机收取的双险种二项风险模型，通过对破产概率的研究 ， 获得了最终破产概率的 Lundberg 不等式和一般表达式。 (4)在保费随机收取的情况下，考虑投资收益因素的影响，建立了带投资和干扰的 具有相关索赔的双险种复合 Poisson 风险模型，给出了破产概率的精确表达式。 关键词：风险模型，破产概率，复合二项风险模型，相关索赔 ABSTRACT The classic risk model is a kind of basic model,But this kind of model could not be applied to practice well.so in this paper we get some genera lized risk model by extend ing the classic risk model in some different aspects and do some researches on them: (l) Consider ing refund event of insurance company,a new binomia l risk model with refund was introduced by popularizing the common binomia l risk model in this paper,Then we discussed the ruin probability and its upper bound of the model. Under the condition of related arriving of premium and cla im,a new compound binomia l risk model with random interest 、interference and random premium was stablished ,A computation of ruin probability on this model was studied by martinga le. Consider ing capital interest rate,we get a more practica l risk model with capital interest by extend ing the binomia l risk model of two-type insurance with mixed premium , Then we discussed the ruin probability and its upper bound of the model. Under the premium is a random variable ,a compound Poisson risk model with two- correla ted cla ims is stablished. Then a computation of ruin probability on this model was studied . Keywords ：Risk model,Ruin probability,Compound binomia l risk model,Two-correla ted cla ims 山东科技大学硕士学位论文目录 山东科技大学硕士学位论文 目录 目 录 1 序言····················································································································1 1.1 破产理论概述······································