Journal of Applied Probability

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

Martin Klimmek

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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.

Article information

J. Appl. Probab., Volume 51, Number 2 (2014), 492-511.

First available in Project Euclid: 12 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60J60: Diffusion processes [See also 58J65]

Inverse problem inverse optimal stopping threshold strategy parameter dependence comparative statics generalised diffusion Gittins index


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.

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