Optimal Learning under Robustness and Time-Consistency

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is timeconsistent. The model is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed-form in two speci…c settings: Ellsberg’s twourn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is the focus. Key words: ambiguity, robust decisions, learning, partial information, optimal stopping, sequential testing of simple hypotheses, Ellsberg Paradox, recursive utility, time consistency, model uncertainty Department of Economics, Boston University, [email protected] and Zhongtai Securities Institute of Financial Studies, Shandong University, [email protected]. Ji gratefully acknowledges the …nancial support of the National Natural Science Foundation of China (award No. 11571203). We received helpful comments from Tomasz Strzalecki and excellent research assistance from Haodong Liu and Fernando Payro.