We consider a stopping problem and its application to the decision-making process regarding the optimal timing of organ transplantation for individual patients. At each decision period, the patient state is inspected and a decision is made whether to transplant. If the organ is transplanted, the process terminates; otherwise, the process continues until a transplant happens or the patient dies. Under suitable conditions, we show that there exists a control limit optimal policy. We propose a smoothed perturbation analysis (SPA) estimator for the gradient of the total expected discounted reward with respect to the control limit. Moreover, we show that the SPA estimator is asymptotically unbiased.

翻译：本文研究一个停止问题及其在个体患者器官移植最佳时机决策过程中的应用。在每个决策周期，评估患者状态并决定是否进行移植。若器官成功移植，则流程终止；否则持续进行，直至完成移植或患者死亡。在适当条件下，我们证明存在最优控制限策略。提出一种针对总期望折现回报关于控制限梯度的平滑扰动分析(SPA)估计量，并证明该SPA估计量具有渐近无偏性。