Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 2 (2014), 492-511.
Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems
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.
J. Appl. Probab., Volume 51, Number 2 (2014), 492-511.
First available in Project Euclid: 12 June 2014
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Klimmek, Martin. Parameter dependent optimal thresholds, indifference levels and inverse optimal stopping problems. J. Appl. Probab. 51 (2014), no. 2, 492--511. doi:10.1239/jap/1402578639. https://projecteuclid.org/euclid.jap/1402578639