An Inverse Optimal Stopping Problem for Diffusion Processes
研究如何找到一个仅依赖于时间的函数π，使得给定的停时τ*是某个最优停时问题的解，并给出了π的唯一性和闭式表示，适用于金融或随机控制中的边界确定问题。
Let X be a one-dimensional diffusion and let g be a real-valued function depending on time and the value of X. This article analyzes the inverse optimal stopping problem of finding a time-dependent real-valued function π depending only on time such that a given stopping time τ ⋆ is a solution of the stopping problem [Formula: see text]. Under regularity and monotonicity conditions, there exists such a transfer π if and only if τ ⋆ is the first time when X exceeds a time-dependent barrier b. We prove uniqueness of the solution π and derive a closed form representation. The representation is based on an auxiliary process that is a version of the original diffusion X reflected at b towards the continuation region. The results lead to a new integral equation characterizing the stopping boundary b of the stopping problem [Formula: see text].