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Quantifying the impact of parametric and model-form uncertainty on thepredictions of stochastic models is a key challenge in many applications.Previous work has shown that the relative entropy rate is an effective tool forderiving path-space uncertainty quantification (UQ) bounds on ergodic averages.In this work we identify appropriate information-theoretic objects for a widerrange of quantities of interest on path-space, such as hitting times andexponentially discounted observables, and develop the corresponding UQ bounds.In addition, our method yields tighter UQ bounds, even in cases where previousrelative-entropy-based methods also apply, e.g., for ergodic averages. Weillustrate these results with examples from option pricing, non-reversiblediffusion processes, stochastic control, semi-Markov queueing models, andexpectations and distributions of hitting times.

Quantification of Model Uncertainty on Path-Space via Goal-Oriented Relative Entropy