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Mathematical Problems in Engineering
Volume 2015, Article ID 134246, 8 pages
Research Article

A Dependent Insurance Risk Model with Surrender and Investment under the Thinning Process

1School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
2School of Science, Shandong Jiaotong University, Jinan 250023, China

Received 26 August 2015; Accepted 17 September 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Wenguang Yu and Yujuan Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A dependent insurance risk model with surrender and investment under the thinning process is discussed, where the arrival of the policies follows a compound Poisson-Geometric process, and the occurrences of the claim and surrender happen as the -thinning process and the -thinning process of the arrival process, respectively. By the martingale theory, the properties of the surplus process, adjustment coefficient equation, the upper bound of ruin probability, and explicit expression of ruin probability are obtained. Moreover, we also get the Laplace transformation, the expectation, and the variance of the time when the surplus reaches a given level for the first time. Finally, various trends of the upper bound of ruin probability and the expectation and the variance of the time when the surplus reaches a given level for the first time are simulated analytically along with changing the investment size, investment interest rates, claim rate, and surrender rate.