Uncertainty Propagation and Dynamic Robust Risk Measures

Marlon R. Moresco (), Mélina Mailhot () and Silvana M. Pesenti ()
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Marlon R. Moresco: Escola de Administração, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul 90010-460, Brazil
Mélina Mailhot: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada
Silvana M. Pesenti: Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3E6, Canada

Mathematics of Operations Research, 2025, vol. 50, issue 3, 1939-1964

Abstract: We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These dynamic uncertainty sets capture the uncertainty surrounding stochastic processes and models, accounting for factors such as distributional ambiguity. Examples of uncertainty sets include those induced by the Wasserstein distance and f -divergences. We further define dynamic robust risk measures as the supremum of all candidates’ risks within the uncertainty set. In an axiomatic way, we discuss conditions on the uncertainty sets that lead to well-known properties of dynamic robust risk measures, such as convexity and coherence. Furthermore, we discuss the necessary and sufficient properties of dynamic uncertainty sets that lead to time-consistencies of dynamic robust risk measures. We find that uncertainty sets stemming from f -divergences lead to strong time-consistency whereas the Wasserstein distance results in a new time-consistent notion of weak recursiveness. Moreover, we show that a dynamic robust risk measure is strong time-consistent or weak recursive if and only if it admits a recursive representation of one-step conditional robust risk measures arising from static uncertainty sets.

Keywords: 91G70; 91G05; 90C39; 49Q22; 90C17; dynamic risk measures; time-consistency; distributional uncertainty; Wasserstein distance (search for similar items in EconPapers)
Date: 2025
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