Volume 55, Number 1, January-February 2021
|Page(s)||131 - 169|
|Published online||18 February 2021|
Quantification of model uncertainty on path-space via goal-oriented relative entropy
Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
* Corresponding author: firstname.lastname@example.org
Accepted: 5 October 2020
Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g., for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times.
Mathematics Subject Classification: 62F35 / 62B10 / 60G40 / 60J60 / 93E20 / 91G20
Key words: Uncertainty quantification / relative entropy / non-reversible diffusion processes / semi-Markov queueing models / stochastic control
© EDP Sciences, SMAI 2021
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