The dividend problem with a finite horizon
The dividend problem with a finite horizon
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有限范围内的股利问题
DOI：
10.1214/17-aap1286
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Erik Ekstrom
中科院分区：
文献类型：
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作者：
T. Angelis;Erik Ekstrom
我们证明了有限时间内最优分红问题的值函数是一个合适的Hamilton-Jacobi-Bellman方程的唯一经典解。最优分红策略是通过在时间依赖的最优边界上对基金价值的Skorokhod反映来实现的。我们的研究结果是通过建立一个新的连接奇异控制问题的吸收边界和最佳停止问题的扩散反映在$0$和创建的速度成比例的当地时间。
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at $0$ and created at a rate proportional to its local time.