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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 ›› 2016, Vol. 33 ›› Issue (5): 463-479.doi: 10.3969/j.issn.1005-3085.2016.05.003

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复合Poisson-Geometric风险下保险公司的最优投资--再保--混合分红策略

孙宗岐1,   陈志平2   

  1. 1- 西安思源学院高数教研室，西安 710038
    2- 西安交通大学数学与统计学院，西安 710049
  • 收稿日期:2016-04-05 接受日期:2016-09-12 出版日期:2016-10-05 发布日期:2016-12-15
  • 基金资助:
    国家自然科学基金 (71371152)；陕西省教育厅2016年度自然科学专项基金 (2016JK2150)；西安思源学院2016年度科研基金 (XASY-B1617).

Optimal Investment-reinsurance-hybrid Dividend Strategies for Insurance Company under Compound Poisson-Geometric Risk Process

SUN Zong-qi1,  CHEN Zhi-ping2   

  1. 1- Department of Mathematics, Xi'an Siyuan University, Xi'an 710038
    2- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2016-04-05 Accepted:2016-09-12 Online:2016-10-05 Published:2016-12-15
  • Supported by:
    The National Natural Science Foundation of China (71371152); the Natural Science Foundation of the Education Department of Shaanxi Province (2016JK2150); the Research Fund of  Xi'an Siyuan College (XASY-B1617).

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摘要： 为了更好地反映保险实际并为保险公司寻求更稳健的策略，本文考虑索赔次数服从复合Poisson-Geometric过程时，保险公司的最优投资--再保--混合分红策略问题．假定保险公司的盈余服从扩散过程，在分红总量现值的期望最大化的准则下，我们使用动态规划原理建立了保险公司的最优投资--再保--混合分红模型，通过求解HJB方程得到了最优投资决策，最后在再保险的保费损失率等于红利的贴现率的条件下，得到了最优投资--再保--混合分红策略的显式解，数值算例及经济分析表明了文章结果的合理性．

关键词: 复合Poisson-Geometric过程, 扩散过程, 投资策略, 再保险策略, 混合分红, HJB方程, 偏离系数

Abstract: To better reflect the insurance prectice and help insurance company making more robust strategy, we assume that the number of claims follows the compound Poisson-Geometric process, and investigate the optimal investment-reinsurance-hybrid dividend problem under the assumption that the insurance's reserve price follows a diffusion process. Based on the criterion of maximizing the expected total present value of dividends, the optimal desicion model is utiliting dynamic programming priciple, and the optimal policy is obtained through solving the HJB equation. The closed-form optimal investment-reinsurance-hybrid dividend strategies have been derived under the special case: the loss rate of reinsurance premiums is equal to the dividend discount rate. Finally, some numerical examples and their economic analyses are provided to illustrate the reasonability of the obtained theoretical results.

Key words: compound Poisson-Geometric process, diffusion process, investment strategy, reinsurance policy, hybrid dividend, HJB equation, deviation coefficient

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