Knightian Forecasting: Mathematical Models of Ambiguity and the Limits of Probabilistic Prediction

Abstract

This paper develops a theoretical framework for forecasting under Knightian uncertainty, where probabilities are not uniquely defined, and ambiguity fundamentally constrains predictive inference. Traditional forecasting relies on single-model probabilistic structures, yet such approaches are often fragile in environments characterized by structural breaks, limited information, and unforeseen shocks. To address this limitation, the study introduces ambiguity envelopes and set-valued forecasts, formalizing predictions that reflect multiple admissible models rather than a single distribution. Building on decision-theoretic foundations, the paper integrates max–min expected utility, variational preferences, and minimax regret to link forecasts directly to robust decision-making. The mathematical models provide empirical foundations for ambiguity-aware forecasting while highlighting implications for evaluation, communication, and practical implementation. The results indicate that forecasting under Knightian uncertainty requires a paradigm shift: moving from precision-oriented prediction toward robustness and resilience. This framework offers a foundation for applying ambiguity-aware forecasting across economics, finance, and policy domains, while it also complements existing robust decision-making methods by providing a formal structure for ambiguity-aware forecast construction within the broader shift from prediction to robustness.