Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (6): 941-948.doi: 10.3969/j.issn.1005-3085.2015.06.015

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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).

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

CLC Number: