论文标题
存在于随机伏尔泰方程的最佳控制
Existence of optimal controls for stochastic Volterra equations
论文作者
论文摘要
我们提供了足够的条件，可以保证在随机伏击方程（SVE）的随机控制问题的弱公式中存在松弛的最佳控制。我们的研究可以应用于当受控SVE中出现的内核以零为零时出现的粗糙过程。放松的最佳策略的存在依赖于可集成性假设在内核上的相互作用与运行成本功能的生长条件与受控SVE的系数之间的相互作用。在经典的凸度假设下，我们还可以推断出最佳严格控制的存在。
We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of stochastic control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes that arise when the kernel appearing in the controlled SVE is singular at zero. The existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel and growth conditions on the running cost functional and the coefficients of the controlled SVEs. Under classical convexity assumptions, we can also deduce the existence of optimal strict controls.
