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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (6): 941-948.doi: 10.3969/j.issn.1005-3085.2015.06.015

• • 上一篇    

比例再保险的双Cox风险模型(英)

贺丽娟1,   王成勇2,   张  锴1   

  1. 1- 文华学院基础学部，武汉 430074
    2- 湖北文理学院数学与计算机科学学院，湖北 襄阳 441053
  • 收稿日期:2014-03-19 接受日期:2015-04-10 出版日期:2015-12-15 发布日期:2016-02-15
  • 基金资助:
    国家自然科学基金 (71371066)；湖北省教学科研项目 (2013448).

A Couple Cox Risk Model about Proportional Reinsurance

HE Li-juan1,   WANG Cheng-yong2,   ZHANG Kai1   

  1. 1- Department of Mathematics, Wenhua College, Wuhan 430074
    2- College of Mathematics & Computer Science, Hubei University of Arts and Science, Xiangyang, Hubei 441053
  • Received:2014-03-19 Accepted:2015-04-10 Online:2015-12-15 Published:2016-02-15
  • Contact: K. Zhang.\quad E-mail address: 23207882@qq.com
  • Supported by:
    The National Natural Science Foundation of China (71371066); the Teaching Research Project of Hubei Province (2013448).

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摘要： 随着保险业务的扩大与发展，保险公司必须购买某些险种的再保险来规避风险．为了研究保险公司购买再保险后的破产概率，本文建立了一个双Cox比例再保险的风险模型．本文假设保费的收取与理赔的发生均为Cox过程，通过鞅方法，利用最优停时定理，我们得到了破产概率的一个上界，并且当理赔发生的累积强度和保费收取的累积强度成正比时，得到了破产概率满足的Lundberg不等式．

关键词: 比例再保险, 双Cox过程, 鞅, 停时, 破产概率

Abstract:

With the expansion and development of insurance business, insurance companies must purchase reinsurance of certain types of insurance to avoid the risk. To study the ruin probability of the insurance company after purchasing the reinsurance, this paper examines the effect of the proportional reinsurance in a couple Cox risk model. The new risk model assumes that both the occurrence of claims and the receiving of premiums follow the Cox processes. We get an upper bound for the ruin probability by using the martingale method and the stopping time criterion, and derive the Lundberg inequality for the ruin probability when the claim sizes follow an exponent distribution and the intensities of couple Cox processes satisfy a linear relation.

Key words: proportional reinsurance, couple Cox process, martingale, stopping time, ruin probability

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