标题： 两种解决受奥恩斯坦-乌伦贝克利率影响的股息最大化问题的方法 显示英文标题

标题： Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

摘要： 我们研究在具有Ornstein-Uhlenbeck动力学的随机利率下的股息最大化问题。 此设置也考虑了负利率的情况。 首先考虑一个确定的时间，其中可以找到显式的分隔曲线$\alpha(t)$来确定时间$t$的最优策略。 在第二种情况下，我们引入了一个与策略无关的停止时间。 这两种情况下的最优控制问题的性质和行为通过分析HJB驱动的方法以及使用倒向随机微分方程进行了分析。 显示英文摘要

摘要： We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve $\alpha(t)$ can be found to determine the optimal strategy at time $t$. In a second setting we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach as well as using backward stochastic differential equations.