Optimal Learning under Robustness and Time Consistency

A decision-maker chooses between actions whose payoffs depend on both exogenous randomness and on an unknown parameter θ. She can postpone the action choice, at a per-unit-time cost, so as to learn about θ by observing the... [ view full abstract ]

A decision-maker chooses between actions whose payoffs depend on both exogenous randomness and on an unknown parameter θ. She can postpone the action choice, at a per-unit-time cost, so as to learn about θ by observing the realization of a signal modeled by a Brownian motion with drift. There is prior ambiguity about θ and the decision-maker seeks to make robust choices of both stopping time and action by solving a maxmin problem. By extending the continuous-time version of maxmin utility in Chen and Epstein (2002) to accommodate learning, the model captures robustness to model uncertainty, learning and time consistency.