标题： 构建与最优停止值一致的时齐广义扩散过程 显示英文标题

标题： Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values

摘要： 考虑一个折扣最优停止问题的集合，针对一个单参数族的目标函数和一个固定的扩散过程，从一个固定点开始。 随机控制/最优停止中的一个标准问题是在此设定下求解问题价值。 在本文中，我们考虑一个反问题；给定一族目标函数的问题价值，我们旨在恢复扩散过程。 在目标函数族的一个自然假设下，我们可以表征存在性和唯一性，使得最优停止问题具有指定的价值。 该问题的解决依赖于广义凸性理论的技术。 显示英文摘要

摘要： Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the problem value in this setting. In this article we consider an inverse problem; given the set of problem values for a family of objective functions, we aim to recover the diffusion. Under a natural assumption on the family of objective functions we can characterise existence and uniqueness of a diffusion for which the optimal stopping problems have the specified values. The solution of the problem relies on techniques from generalised convexity theory