论文标题
在随机控制问题上
On the Stochastic Control-Stopping Problem
论文作者
论文摘要
当数据具有多项式生长时，我们研究了随机控制问题。该方法基于向后的随机差异方程（简称BSDE）。该问题变成了针对特定的BSDE的研究，并具有随机Lipschitz系数，我们显示了溶液的存在和独特性。然后，我们与控制问题的价值函数建立了关系。展示了最佳策略。最后，在马尔可夫框架中，我们证明了值函数是相关的汉密尔顿 - 雅各比 - 贝尔曼方程的唯一粘度解。
We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a stochastic Lipschitz coecient for which we show existence and uniqueness of the solution. We then establish its relationship with the value function of the control-stopping problem. The optimal strategy is exhibited. Finally in the Markovian framework we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.
