Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems
Probability
2013-02-13 v1 Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.1302.2769,
title = {Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems},
author = {Martin Klimmek},
journal= {arXiv preprint arXiv:1302.2769},
year = {2013}
}