arXiv 28 Jun 2026 · Finance — Mathematical Finance
arXiv:2606.29572 · PDF · DOI · OpenAlex · Extracted main text
This paper studies the recovery of uncertainty from dynamic sublinear valuation rules. A robust valuation assigns each payoff its worst-case expected value across plausible models under uncertainty and induces a dynamic sublinear valuation rule. While valuation rules are observable in practice, the underlying uncertainty structure is latent. First, we show that the latent uncertainty structure can be identified from an observed valuation rule and provide an explicit procedure for recovering it. Second, we develop the notion of time consistency for uncertainty structures as the uncertainty-side counterpart of time consistency in valuation. Third, we characterize all time-consistent uncertainty structures that represent a given valuation rule. Finally, we develop nonparametric estimators for recovering uncertainty from limited valuation data. These results overturn the traditional Knightian view that uncertainty is inherently non-measurable. Indeed, valuation contains sufficient information to identify, characterize, and statistically recover the uncertainty structures that generate it.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Nutz, M. and Van Handel, R (2013) Constructing sublinear expectations on path space | 0.737 | 3 | 3 | 67% |
| 2 | Pinsky, R. G (1995) Positive harmonic functions and diffusion, volume 45 | 0.693 | 6 | 4 | 33% |
| 3 | Cheridito, P., Delbaen, F., and Kupper, M (2006) Dynamic monetary risk measures for bounded discrete-time processes | 0.644 | 2 | 2 | 100% |
| 4 | Epstein, L. G. and Schneider, M (2003) Recursive multiple-priors | 0.644 | 2 | 2 | 100% |
| 5 | Knight, F. H (1921) Risk, uncertainty and profit, volume 31 | 0.644 | 2 | 2 | 100% |
| 6 | Crandall, M. G., Ishii, H., and Lions, P.-L (1992) User’s guide to viscosity solutions of second order partial differential equations | 0.511 | 3 | 2 | 33% |
| 7 | Anderson, E. W., Hansen, L. P., and Sargent, T. J (2003) A quartet of semigroups for model specification, robustness, prices of risk, and model detection | 0.405 | 1 | 1 | 100% |
| 8 | Chen, Z. and Epstein, L. G (2002) Ambiguity, risk, and asset returns in continuous time | 0.405 | 1 | 1 | 100% |
| 9 | Crandall, M. G., Kocan, M., and Świech, A (2000) $L^p$-theory for fully nonlinear uniformly parabolic equations: Parabolic equations | 0.405 | 1 | 1 | 100% |
| 10 | Criens, D. and Kupper, M (2025) Representation theorems for convex expectations and semigroups on path space | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 36 scored citations.