具有无界折扣率的折扣报酬控制问题的光滑解及其金融应用
Smooth solutions to discounted reward control problems with unbounded discount rate and financial applications
摘要：
考虑连续时间随机环境中的折扣报酬控制问题，其中折扣率可能是控制过程的无界函数。我们提供了一组一般的假设，以确保存在一个光滑的经典解相应的HJB方程。此外，提供了一些验证推理，并讨论了可能的扩展到动态游戏。文章最后还对金融经济学中的消费-投资问题进行了思考.
英文摘要：
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verification reasoning are provided and the possible extension to dynamic games is discussed. At the end of the paper consumption - investment problems arising in financial economics are considered.
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