Some results on the Gittins index for a normal reward process

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dc.creatorYao, Yi-Ching
dc.date2007-02-27
dc.date.accessioned2026-07-07T08:08:48Z
dc.date.available2026-07-07T08:08:48Z
dc.descriptionWe consider the Gittins index for a normal distribution with unknown mean $θ$ and known variance where $θ$ has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation to the Gittins index by embedding the (discrete-time) normal setting into the continuous-time Wiener process setting in which the Gittins index is determined by the stopping boundary for an optimal stopping problem. By an application of Chernoff's continuity correction in optimal stopping, the approximation includes a correction term which accounts for the difference between the discrete and continuous-time stopping boundaries. Numerical results are also given to assess the performance of this simple approximation.
dc.descriptionPublished at http://dx.doi.org/10.1214/074921706000001111 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0702831
dc.identifierhttp://arxiv.org/abs/math/0702831
dc.identifierIMS Lecture Notes Monograph Series 2006, Vol. 52, 284-294
dc.identifierdoi:10.1214/074921706000001111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131387
dc.subjectStatistics Theory
dc.subject60G40 (Primary) 90C39 (Secondary)
dc.titleSome results on the Gittins index for a normal reward process
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