论文标题
有限的视野最佳随机冲动控制问题，决策滞后
A Finite Horizon Optimal Stochastic Impulse Control Problem with A Decision Lag
论文作者
论文摘要
本文在有限的地平线上研究了一个最佳的随机冲动控制问题，而决策滞后，我们的意思是在脉冲后，必须在允许下一个脉冲之前经过固定的时间单位。证明了价值函数的连续性。建立了合适的动态编程原则，该版本考虑了状态过程对经过的时间的依赖性。得出了相应的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程，该方程表现出了一些特殊的问题。此最佳冲动控制问题的价值函数被表征为相应HJB方程的唯一粘度解决方案。只要给出了值函数，就可以构建最佳的冲动控制。此外，讨论了等待时间接近$ 0 $的限制案例。
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to be made. The continuity of the value function is proved. A suitable version of dynamic programming principle is established, which takes into account the dependence of state process on the elapsed time. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is derived, which exhibit some special feature of the problem. The value function of this optimal impulse control problem is characterized as the unique viscosity solution to the corresponding HJB equation. An optimal impulse control is constructed provided the value function is given. Moreover, a limiting case with the waiting time approaching $0$ is discussed.
