Controlled McKean-Vlasov Problems without Weak Monotonicity

Definitions and mathematical statement

A controlled McKean--Vlasov problem concerns a controlled stochastic system whose dynamics depend on a probability law associated with the system. The supplied record does not specify the state space, the relevant law, the dynamics, the admissible controls, or the mathematical conclusion under consideration. In particular, it does not define the inequalities called weak monotonicity conditions.

Source-relative problem. In the controlled McKean--Vlasov theory referenced by the cited workshop contribution, relax some of the weak monotonicity conditions imposed in the contribution's reference [3], while retaining the corresponding mathematical conclusions under the remaining hypotheses. The supplied clean statement additionally asks whether these hypotheses can be removed altogether; the supplied original excerpt explicitly asks only to relax some of them.

This is an unresolved formulation specification: reference [3], its hypotheses, and its conclusions are not reproduced in the supplied record. Consequently, no particular monotonicity inequality, domain, boundary condition, quantifier structure, or replacement hypothesis can be stated reliably from the supplied evidence. This draft records the research question and does not assert a theorem or identify a specific admissible weakening.

Short English statement

The problem asks whether some weak monotonicity assumptions in a referenced controlled McKean--Vlasov theory can be relaxed. The supplied clean statement also asks about removing them. The underlying assumptions and results are missing, so a precise theorem-level formulation requires checking the cited workshop contribution and its reference [3].

Sources

• Local UnsolvedMath registry, supplied complete source record: permanent ID 30005689, source problem code catalogue entry, title Controlled McKean--Vlasov Problems without Weak Monotonicity; collection: Oberwolfach Reports Open Problems. The supplied proposed year is 2023; no proposer is named.
• Supplied authoritative report citation: New Challenges in the Interplay between Finance and Insurance (2024), Oberwolfach Reports, pp. 2547--2635, DOI 10.4171/owr/2023/44. https://doi.org/10.4171/owr/2023/44. The supplied original excerpt is associated with p. 2627 and refers to relaxing some weak monotonicity conditions from reference [3]; that reference's bibliographic entry is not supplied.
• Supplied literature source labelled "Criens": https://arxiv.org/abs/2310.00928. No title, theorem number, or explicit identification with reference [3] is provided.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the problem open, states that the report explicitly records relaxation of the weak monotonicity conditions as an open problem, and reports that no complete primary resolution was found. Both links above are listed as sources checked. This is supplied dated curation, not an independently verified literature assessment.
• The registry labels the statement corrected_verified and supplies a claim that it was checked against the official report and preserves its hypotheses, notation, and target. These are supplied verification claims; no independent source consultation or mathematical verification is asserted here.