英文标题：
《Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints
  on Dividend Rates》
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作者：
Bahman Angoshtari, Erhan Bayraktar, Virginia R. Young
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最新提交年份：
2019
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英文摘要：
  We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal Duesenberry\'s ratcheting consumption problem, studied by Dybvig (1995) [Review of Economic Studies 62(2), 287-313], in which consumption is assumed to be nondecreasing. Our problem differs from Dybvig\'s also in that the time of ruin could be finite in our setting, whereas ruin was impossible in Dybvig\'s work. We formulate our problem as a stochastic control problem with the objective of maximizing the expected discounted utility of the dividend stream until bankruptcy, in which risk preferences are embodied by power utility. We semi-explicitly solve the corresponding Hamilton-Jacobi-Bellman variational inequality, which is a nonlinear free-boundary problem. The optimal (excess) dividend rate $c^*_t$ - as a function of the company\'s current surplus $X_t$ and its historical running maximum of the (excess) dividend rate $z_t$ - is as follows: There are constants $0 < w_{\\alpha} < w_0 < w^*$ such that (1) for $0 < X_t \\le w_{\\alpha} z_t$, it is optimal to pay dividends at the lowest rate $\\alpha z_t$, (2) for $w_{\\alpha} z_t < X_t < w_0 z_t$, it is optimal to distribute dividends at an intermediate rate $c^*_t \\in (\\alpha z_t, z_t)$, (3) for $w_0 z_t < X_t < w^* z_t$, it is optimal to distribute dividends at the historical peak rate $z_t$, (4) for $X_t > w^* z_t$, it is optimal to increase the dividend rate above $z_t$, and (5) it is optimal to increase $z_t$ via singular control as needed to keep $X_t \\le w^* z_t$. Because, the maximum (excess) dividend rate will eventually be proportional to the running maximum of the surplus, \"mountains will have to move\" before we increase the dividend rate beyond its historical maximum.
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中文摘要：
我们考虑了一个习惯形成约束下的最优股息问题，该约束防止股息率低于其历史最大值的一定比例，即所谓的提取约束。这是Dybvig（1995）[经济研究回顾62（2），287-313]研究的最优Duesenberry棘轮消费问题的扩展，其中假设消费是非减量的。我们的问题与Dybvig的不同之处还在于，在我们的环境中，破产的时间可能是有限的，而在Dybvig的工作中，破产是不可能的。我们将问题描述为一个随机控制问题，目标是在破产前最大化股息流的预期贴现效用，其中风险偏好由幂效用体现。我们半显式地求解相应的Hamilton-Jacobi-Bellman变分不等式，这是一个非线性自由边界问题。最佳（超额）股息率$c ^*\\u t$-作为公司当前盈余$X\\u t$及其历史运行最大（超额）股息率$z\\u t$的函数如下：存在常数$0<w\\u{\\alpha}<w\\u 0<w ^*$，因此（1）对于$0<X\\u{\\alpha}z\\u t$，以最低利率$z\\u t$支付股息是最佳的，（2）对于$w\\u{\\alpha}z\\u t<X\\u t<w\\u 0 z\\u t$，以中间利率$c^*\\t\\in（\\ alpha z\\u t，z\\u t）$，（3）对于$w\\u 0 z\\u t<X\\u t<w^*z\\u t$，以历史峰值利率$z\\u t$分配股息是最佳的，（4）对于$X\\u t>w^*z\\u t$，将股息率提高到$z\\u t$以上是最佳的，并且（5）根据需要通过单一控制增加$z\\u t$，以保持$X\\u t\\le w是最佳的^*z\\U美元。因为，最大（超额）股息率最终将与盈余的运行最大值成比例，“大山将不得不移动”，然后我们将股息率提高到历史最大值以上。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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