Some results on the Gittins index for a normal reward process

Details Some results on the Gittins index for a normal reward process Some results on the Gittins index for a normal reward process

2007-02-27

arxiv.org/abs/math/0702831v1

IMS Lecture Notes Monograph Series 2006, Vol. 52, 284-294

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000001111 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000001111

We consider the Gittins index for a normal distribution with unknown mean $\theta$ and known variance where $\theta$ 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.

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