We consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then apply this result to solve an impulse control problem for stochastic delay differential equations driven by a Brownian motion and an independent compound Poisson process. Furthermore, we show that the studied problem arises naturally when maximizing the revenue from operation of a group of hydro-power plants with hydrological coupling.

中文翻译：

---

具有存储器的有限水平最优切换问题及其在受控SDDE中的应用

我们考虑一个最优的切换问题，其中终端奖励取决于整个控制轨迹。我们通过应用基于Snell包络概念的概率技术来显示最优控制的存在。然后，我们将这个结果用于解决由布朗运动和独立复合泊松过程驱动的随机时滞微分方程的脉冲控制问题。此外，我们表明，当最大化一组具有水文耦合的水力发电厂的运营收益时，自然会出现所研究的问题。