Relaxing Endpoint Conditions in Affine Volatility Large Deviations

Definitions and mathematical statement

The supplied record concerns a large-deviation principle for affine stochastic-volatility models and singles out the endpoint matching hypothesis \[ w(u_+)=w(u_-). \] Here $w$, $u_-$, and $u_+$ are notation retained from the source record. Their definitions, domains, and endpoint evaluation conventions are not supplied; in particular, it is unspecified whether these values are ordinary evaluations, one-sided limits, or extended-real quantities.

Statement of the requested problem. Determine whether the hypothesis $w(u_+)=w(u_-)$ can be weakened or omitted in the intended large-deviation theorem for affine stochastic-volatility models, and identify replacement hypotheses under which that theorem's large-deviation conclusion remains valid, with its other hypotheses retained.

Unresolved qualifications. The intended theorem and its remaining hypotheses are not stated. The record does not specify the stochastic model equations, admissible parameters, initial or boundary conditions, random quantities satisfying the large-deviation principle, asymptotic regime, normalization, speed, rate function, or state space and topology. Consequently, the question above preserves the supplied target but cannot yet be expressed as a fully specified quantified mathematical assertion. No particular model class, endpoint convention, or replacement hypothesis is selected in this draft.

Short English statement

The problem asks whether an endpoint matching assumption in an affine stochastic-volatility large-deviation theorem can be relaxed, and what assumptions could replace it. The supplied record omits the theorem and the definitions of its endpoint notation, so a precise theorem-level formulation requires further source clarification. Its partially_solved label is supplied dated curation, not an independently verified mathematical conclusion.

Sources

• Supplied local registry record, permanent UnsolvedMath ID $30003432$, source problem code catalogue entry, titled "Relaxing Endpoint Conditions in Affine Volatility Large Deviations." The collection attributes the question to Oberwolfach Reports workshop discussions; no individual proposer is supplied. The recorded proposed year is 2017.
• Supplied report citation: Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769. https://doi.org/10.4171/owr/2017/13. The supplied citation names 2018, whereas the DOI and proposed-year metadata contain 2017; this discrepancy remains unresolved. No theorem number or pinpoint location for the endpoint condition is supplied.
• Supplied literature reference: Grbac--Krief--Tankov, "trajectorial large deviations." https://arxiv.org/abs/1809.06153.
• Supplied literature reference: Gulisashvili, "large deviations for Volterra volatility." https://doi.org/10.1137/17M116344X.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem partially solved and reports extensions of large-deviation results to broad affine and Volterra stochastic-volatility classes, while describing the particular endpoint matching assumption as restrictive and lacking a general necessary-and-sufficient relaxation. This is supplied dated curation derived from the OWR record, not independently verified here; the source itself requests independent verification of time-sensitive status and cited claims.
• The registry assigns corrected_verified statement status and says that notation, typography, and sentence structure were repaired while preserving mathematical content. These are supplied editorial assertions, not independent mathematical verification of this draft.