Optimal detection of a hidden target: The median rule

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Peskir, Goran

关键词: Optimal stopping;    Hidden target;    Rolling median/quantile rule;    Lagrange multiplier;   

DOI  :  10.1016/j.spa.2012.02.004

来源: Elsevier

【 摘 要 】

We show that in the absence of any information about the 'hidden' target in terms of the observed sample path, and irrespectively of the distribution law of the observed process, the 'median' rule is optimal in both the space domain and the time domain. While the fact that the median rule minimises the spatial expectation can be seen as a direct extension of the well-known median characterisation dating back to Boscovich, the fact that this also holds for the temporal expectation seems to have stayed unnoticed until now. Building on this observation we derive new classes of median/quantile rules having a dynamic character. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free