Robust Maximum Detection: Full Information Best Choice Problem under Multiple Priors

Lazar Obradović
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Lazar Obradović: Center for Mathematical Economics, Bielefeld University

No 580, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We consider a robust version of the full information best choice problem (Gilbert and Mosteller (1966)): there is ambiguity (represented by a set of priors) about the measure driving the observed process. We solve the problem under a very general class of multiple priors in the setting of Riedel (2009). As in the classical case, it is optimal to stop if the current observation is a running maximum that exceeds certain thresholds. We characterize the decreasing sequence of thresholds, as well as the (history dependent) minimizing measure. We introduce locally constant ambiguity neighborhood (LCAn) which has connections to coherent risk measures. Sensitivity analysis is performed using LCAn and exponential neighborhood from Riedel (2009).

Pages: 39
Date: 2018-01-22
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