The Most Dangerous Model : A Natural Benchmark for Assessing Model Risk

We examine the problem of decision making using a probabilistic model when there is material uncertainty concerning the accuracy of the model coupled with limited information about it. Such conditions could hold, for example, for the user of a complex commercial model of natural catastrophe insurance risk. Working within an ambiguity-averse decision framework, we define bounds for a set of plausible alternative models, centered on the “baseline” model provided to the user. Three types of bounds are defined, reflecting the model user's assumptions about the unknown and inaccessible data to which the baseline model was fit. Given a utility function for a decision option and a bound, we first address the corresponding optimization problem of finding the “worst” (most adverse expected utility) model within the set of plausible models. Second, we construct posterior mean utilities among the unbounded set of alternatives and show the existence of a posterior utility-minimizing worst credible model, i.e. the “most dangerous model.” Among all alternative models to the baseline, this model has the highest product of expected disutility times probability that it, and not the baseline, is the correct model. We present a case study of how the most dangerous model can be used as a naturally occurring benchmark when making decisions in the presence of model risk