论文标题
布朗风险模型中股息的最佳棘轮
Optimal ratcheting of dividends in a Brownian risk model
论文作者
论文摘要
我们研究了由布朗尼运动控制的剩余过程中最佳股息支出的问题，并在棘轮的附加约束下漂移，即股息利率永远不会降低。我们解决了由此产生的二维最佳控制问题，将值函数识别为相应的汉密尔顿 - 雅各比 - 贝尔曼方程的唯一粘度解。对于有限的许多可接受的股息利率，我们证明了阈值策略是最佳的，对于任何有限的可接受的股息率连续性，我们确定了曲线策略的$ \ varepsilon $ oftimality。这项工作是Albrecher等人的对应物。 （2020），研究了棘轮问题，以用于漂移的复合泊松盈余过程。在当前的布朗安装中，变异技术的计算允许获得更明确的分析和最佳股息策略的描述。我们还给出了一些数值插图，以了解最佳结果。
We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e. the dividend rate can never decrease. We solve the resulting two-dimensional optimal control problem, identifying the value function to be the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. For finitely many admissible dividend rates we prove that threshold strategies are optimal, and for any finite continuum of admissible dividend rates we establish the $\varepsilon$-optimality of curve strategies. This work is a counterpart of Albrecher et al. (2020), where the ratcheting problem was studied for a compound Poisson surplus process with drift. In the present Brownian setup, calculus of variation techniques allow to obtain a much more explicit analysis and description of the optimal dividend strategies. We also give some numerical illustrations of the optimality results.
