参数依赖的最优阈值、无差异水平和逆最优停止问题
Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems
摘要：
考虑经典的无限时域问题，即停止一维扩散以在运行和终端奖励之间进行优化，并假设我们给出了一个参数化的此类问题。我们提供了一个一般的理论，参数依赖的阈值策略是最佳的无限地平线停止问题。该方法的关键是一个超模块性条件，保证家庭的问题是可索引的集值映射，我们称之为无差异映射。该图是分配（Gittins）指数的自然概括，分配（Gittins）指数是动态分配理论中的经典数量。重要的是，索引的概念导致了一个框架，逆最优停止问题。
英文摘要：
Consider the classic infinite-horizon problem of stopping a one-dimensional diffusion to optimise between running and terminal rewards and suppose we are given a parametrised family of such problems. We provide a general theory of parameter dependence in infinite-horizon stopping problems for which threshold strategies are optimal. The crux of the approach is a supermodularity condition which guarantees that the family of problems is indexable by a set valued map which we call the indifference map. This map is a natural generalisation of the allocation (Gittins) index, a classical quantity in the theory of dynamic allocation. Importantly, the notion of indexability leads to a framework for inverse optimal stopping problems.
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