论文标题
吸收及其在股息问题上的奇异控制中的最大原理
The maximality principle in singular control with absorption and its applications to the dividend problem
论文作者
论文摘要
由经典股息问题的新表述激发，我们表明佩斯基尔的最大原理可以转移到具有二维退化动力学和沿状态空间对角线的二维退化动力学和吸收的奇异随机控制问题。我们将最佳控制构建为沿移动屏障的Skorokhod反射，在该屏障可以分析地计算为某些非线性普通微分方程的最小解决方案。与股息问题的经典一维公式相反，当公司的（分割前）股票资本随着几何布朗尼运动而演变时，我们的框架会产生非平凡的解决方案。这种解决方案在质上与传统上获得的算术布朗运动的解决方案也有所不同。
Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with 2-dimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain non-linear ordinary differential equation. Contrarily to the classical 1-dimensional formulation of the dividend problem, our framework produces a non-trivial solution when the firm's (pre-dividend) equity capital evolves as a geometric Brownian motion. Such solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
