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arXiv · 1302.2769

Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems

Martin Klimmek
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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.

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Martin Klimmek. 2013-02-12. Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems. https://arxiv.org/abs/1302.2769

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