非线性红利边界下的扰动风险模型
发布时间：2019-04-19 16:27
【摘要】：为了降低未来风险所带来的损失，保险行业应运而生，，然而传统的风险模型已经无法准确描述保险公司经营的现实情况，比如说现实中我们要考虑到分红因素，因此关于带有红利边界的风险模型的研究越来越被关注。 本文首先介绍了保险行业发展的背景和研究状况，然后以经典风险模型为基础，提出了一种新的风险模型：在非线性红利边界的分红策略下考虑市场因素，加入扰动项，使模型能够准确描述保险公司经营的现实情况，利用索赔时间的强马氏性和全概率公式给出了该模型下的最终生存概率和折罚函数所满足的微分-积分方程，并给出证明。进一步在此基础上引入绝对破产的概念，同样推导出此模型的Gerber-Shiu折现罚金函数满足的微分-积分方程。
[Abstract]:In order to reduce the losses caused by the future risks, the insurance industry came into being. However, the traditional risk model has not been able to accurately describe the reality of the operation of insurance companies, for example, we should consider the dividend factor in reality. Therefore, more and more attention has been paid to the study of risk models with dividend boundary. This paper first introduces the background and research status of insurance industry development, then based on the classical risk model, puts forward a new risk model: considering the market factor and adding disturbance term under the non-linear dividend boundary dividend strategy, and then based on the classical risk model, this paper presents a new risk model based on the classical risk model. By using the strong Markov property of claim time and the total probability formula, the differential-integral equation satisfied by the final survival probability and penalty function under the model is given, and the proof is given. On this basis, the concept of absolute ruin is introduced, and the Integro-differential equations satisfied by the Gerber-Shiu discounted penalty function of the model are also derived.
【学位授予单位】：武汉科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224
本文编号：2461106
[Abstract]:In order to reduce the losses caused by the future risks, the insurance industry came into being. However, the traditional risk model has not been able to accurately describe the reality of the operation of insurance companies, for example, we should consider the dividend factor in reality. Therefore, more and more attention has been paid to the study of risk models with dividend boundary. This paper first introduces the background and research status of insurance industry development, then based on the classical risk model, puts forward a new risk model: considering the market factor and adding disturbance term under the non-linear dividend boundary dividend strategy, and then based on the classical risk model, this paper presents a new risk model based on the classical risk model. By using the strong Markov property of claim time and the total probability formula, the differential-integral equation satisfied by the final survival probability and penalty function under the model is given, and the proof is given. On this basis, the concept of absolute ruin is introduced, and the Integro-differential equations satisfied by the Gerber-Shiu discounted penalty function of the model are also derived.
【学位授予单位】：武汉科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224
【参考文献】
相关期刊论文 前10条
1 洪圣光;赵秀青;;再保险的COX风险模型[J];长春工程学院学报(自然科学版);2008年02期
2 龚日朝,杨向群;复合广义Poisson模型下最终破产概率估计[J];长沙电力学院学报(自然科学版);2001年01期
3 范庆祝;尹传存;;带红利的两类索赔风险模型的Gerber-Shiu函数[J];工程数学学报;2009年01期
4 刘向增;田铮;张燕;;常利率下有阈红利边界的Erlang(2)风险模型的罚金折现期望函数[J];工程数学学报;2010年02期
5 陈新美;;随机利率下广义复合Poisson风险模型[J];长沙理工大学学报(自然科学版);2006年02期
6 罗琰,邹捷中;一类离散双险种风险模型[J];数学理论与应用;2004年03期
7 高珊;一类带干扰的Cox风险模型[J];贵州师范大学学报(自然科学版);2005年03期
8 李棵;赵晓芹;;多因素影响下的三非齐次Poisson风险模型[J];数学理论与应用;2013年01期
9 陈珊萍,王过京,王振羽;稀疏过程在保险公司破产问题中的应用[J];数理统计与管理;2001年05期
10 董亚娟,朱勇华;保险系统中一种推广风险模型的破产概率[J];数学的实践与认识;2004年06期
本文编号：2461106
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2461106.html
