论文标题
从离散到连续最佳投资停止问题的收敛率
The convergence rate from discrete to continuous optimal investment stopping problem
论文作者
论文摘要
我们在连续和离散案例中研究了最佳的投资停止问题，在这些情况下，投资者需要选择最佳交易策略和最佳停止时间，以同时同时最大化终端财富的预期效用。基于具有附加随机收益函数的工作[9]，我们通过二次反射的后向随机微分方程（简称BSDE）的理论来表征连续问题的价值函数，并具有无界的终端条件。关于离散问题，我们获得了由马尔可夫框架和有限障碍物的假设递归的分段二次BSDE组成的离散形式，并在辅助前进的SDE SDE系统和Malliavin Claculus的帮助下提供了有关解决方案的一些有用的先验估计。最后，我们从离散到连续二次反映的BSDE获得统一的收敛和相关率，这是由于相应的最佳投资阻止问题而引起的，通过上述表征。
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth. Based on the work [9] with an additional stochastic payoff function, we characterize the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equation (BSDE for short) with unbounded terminal condition. In regard to discrete problem, we get the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provide some useful prior estimates about the solutions with the help of auxiliary forward-backward SDE system and Malliavin calculus. Finally, we obtain the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.
