Abstract
Consider the classic infinite-horizon problem of stopping a one-dimensional diffusion to optimise between running and terminal rewards, and suppose that 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.
Citation
Martin Klimmek. "Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems." J. Appl. Probab. 51 (2) 492 - 511, June 2014. https://doi.org/10.1239/jap/1402578639
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