Quantifying ambiguity bounds via time-consistent sets of indistinguishable models

Models can be wrong and recognizing their limitations is important in financial and economic decision making under uncertainty. Robust strategies, which are least sensitive to perturbations of the underlying model, take uncertainty into account. Interpreting the explicit set of alternative models surrounding the baseline model has been difficult so far. We specify alternative models via a time-consistent set of equivalent probability measures and derive a quantitative bound on the uncertainty set. We find an explicit ex ante relation between the size of this set, and the Type I and II error probabilities on the statistical test that is hypothetically performed to investigate whether the alternative model specification could be rejected at a future test horizon. The hypothetical test is constructed to obtain all alternative models that are indistinguishable from the baseline model. We also link the ambiguity bound, which is now a function of interpretable variables, to numerical values on several divergence measures and illustrate our methodology on a robust investment problem.