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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (2): 159-170    DOI:
    
Perturbed Markov-modulated dual risk model with constant dividend barrier
LIU Dong-hai1, PENG Dan1, LIU Zai-ming2
1. Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, China
2. Department of Mathematics, Central South University, Changsha 410075, China
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Abstract  The paper discusses a perturbed Markov-modulated dual risk model with constant dividend barrier, in which, the gain arrivals, gains sizes and expenses are influenced by a Markov process. A system of integro-differential equations for the expected total discounted dividend payments until ruin is derived. Moreover, in the two-state model, explicit results are obtained when both claim amounts are exponentially distributed and mixed exponentially distributed. Finally, some numerical examples are given.

Key words： dual risk model      Markov-modulated      integro-differential equation      the expected total discounted dividend payments     
Received: 25 November 2013      Published: 28 July 2018
CLC:  O211.6  
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Cite this article:

LIU Dong-hai, PENG Dan, LIU Zai-ming. Perturbed Markov-modulated dual risk model with constant dividend barrier. Applied Mathematics A Journal of Chinese Universities, 2014, 29(2): 159-170.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I2/159


常数分红界下带扰动的马氏调制对偶风险模型

考虑常数分红界下带扰动的马尔可夫调制对偶风险模型, 其中保险公司收益到达过程、收益额的大小以及支出都受一马尔可夫过程的影响, 得到了破产前累积分红折现均值所满足的积分-微分方程及边界条件; 进一步得到了两状态下, 收益分布为指数分布和混合指数分布时累积分红折现均值的表达式, 最后给出了数值模拟实例.

关键词： 对偶风险模型,  马氏调制,  积分-微分方程,  累积分红折现均值 
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