| 带资本注入、交易费和税的经典风险模型的最优联合分红与注资策略（英文） |
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| 引用本文： | 张爱丽,刘章,王文元,胡亦钧. 带资本注入、交易费和税的经典风险模型的最优联合分红与注资策略（英文）[J]. 应用概率统计, 2019, 0(1): 1-27 |
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| 作者姓名： | 张爱丽 刘章 王文元 胡亦钧 |
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| 作者单位： | 南京审计大学理学院;江西农业大学理学院;武汉大学数学与统计学院;新疆财经大学应用数学学院;厦门大学数学科学学院 |
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| 基金项目： | supported in part by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20151459);the National Natural Science Foundation of China(Grant Nos.11526112;11771343);the Science and Technology Planning Project of Jiangxi Provincial Education Department(Grant No.GJJ150401);the Open Issue of Financial Engineering Key Laboratory of Jiangsu Province of China(Grant No.NSK2015-17) |
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| 摘 要： | 在风险理论中,经典Cramér-Lundberg模型的最优红利策略和最优红利收益函数问题是一个被广泛讨论的话题.本文讨论一类Cramér-Lundberg模型:其在分红时伴随比例赋税与固定交易费,注资时伴随比例罚金与固定交易费,并研究了其净红利收益与注入资本之差的预期贴现值的最大化问题.这里我们不允许负盈余或破产的发生.通过解相应的拟变分不等式,在索赔为指数分布时,得到了最优收益函数和最优联合分红与注资策略的解析解.
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| 关 键 词： | 脉冲随机控制 红利 资本注入 税收 拟变分不等式 |
Impulse Stochastic Control for the Optimal Dividend Policy in a Classical Risk Model with Capital Injection,Transaction Costs and Taxes |
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| ZHANG Aili,LIU Zhang,WANG Wenyuan,HU Yijun. Impulse Stochastic Control for the Optimal Dividend Policy in a Classical Risk Model with Capital Injection,Transaction Costs and Taxes[J]. Chinese Journal of Applied Probability and Statisties, 2019, 0(1): 1-27 |
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| Authors: | ZHANG Aili LIU Zhang WANG Wenyuan HU Yijun |
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| Affiliation: | (Faculty of Science,Nanjing Audit University,Nanjing,211815,China;College of Sciences,Jiangxi Agricultural University,Nanchang,330045,China;School of Mathematics and Statistics,Wuhan University,Wuhan,430072,China;School of Applied Mathematics,Xinjiang University of Finance and Economics,Wulumuqi,830012,China;School of Mathematical Sciences,Xiamen University,Xiamen,361005,China) |
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| Abstract: | In the classical Cramer-Lundberg model in risk theory the problem of finding the optimal dividend strategy and optimal dividend return function is a widely discussed topic.In the present paper,we discuss the problem of maximizing the expected discounted net dividend payments minus the expected discounted costs of injecting new capital,in the Cramer-Lundberg model with proportional taxes and fixed transaction costs imposed each time the dividend is paid out and with both fixed and proportional transaction costs incurred each time the capital injection is made.Negative surplus or ruin is not allowed.By solving the corresponding quasi-variational inequality,we obtain the analytical solution of the optimal return function and the optimal joint dividend and capital injection strategy when claims are exponentially distributed. |
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| Keywords: | impulse stochastic control dividend capital injection taxes quasi-variational inequality |
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