Matches in SemOpenAlex for { <https://semopenalex.org/work/W3204306733> ?p ?o ?g. }
Showing items 1 to 97 of
97
with 100 items per page.
- W3204306733 abstract "In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the conditional law $E[X_t|mathcal{F}_t^Y]$ of the state process conditioned with respect to the past of observation process $Y$. We first deduce the well-posedness of the controlled system by showing weak existence and uniqueness in law. Neither supposing convexity of the control state space nor differentiability of the coefficients with respect to the control variable, we study Peng's stochastic maximum principle for our control problem. The novelty and the difficulty of our work stem from the fact that, given an admissible control $u$, the solution of the associated control problem is only a weak one. This has as consequence that also the probability measure in the solution $P^{u}=L^{u}_TQ$ depends on $u$ and has a density $L^{u}_T$ with respect to a reference measure $Q$. So characterizing an optimal control leads to the differentiation of non-linear functions $f(P^{u}circ{E^{P^{u}}[X_t|mathcal{F}_t^Y]}^{-1})$ with respect to $(L^{u}_T,X_t)$. This has as consequence for the study of Peng's maximum principle that we get a new type of first and second order variational equations and adjoint backward stochastic differential equations, all with new mean-field terms and with coefficients which are not Lipschitz. For their estimates and for those for the Taylor expansion new techniques have had to be introduced and rather technical results have had to be established. The necessary optimality condition we get extends Peng's one with new, non-trivial terms." @default.
- W3204306733 created "2021-10-11" @default.
- W3204306733 creator A5032538768 @default.
- W3204306733 creator A5074307078 @default.
- W3204306733 creator A5090630579 @default.
- W3204306733 date "2021-09-25" @default.
- W3204306733 modified "2023-09-27" @default.
- W3204306733 title "A stochastic maximum principle for partially observed general mean-field control problems with only weak solution" @default.
- W3204306733 cites W1554577510 @default.
- W3204306733 cites W1971754637 @default.
- W3204306733 cites W1973258650 @default.
- W3204306733 cites W1977937811 @default.
- W3204306733 cites W1987280177 @default.
- W3204306733 cites W2017032949 @default.
- W3204306733 cites W2033603136 @default.
- W3204306733 cites W2038686546 @default.
- W3204306733 cites W2038912457 @default.
- W3204306733 cites W2041869614 @default.
- W3204306733 cites W2048138547 @default.
- W3204306733 cites W2068168851 @default.
- W3204306733 cites W2138405426 @default.
- W3204306733 cites W2738289186 @default.
- W3204306733 cites W2952444919 @default.
- W3204306733 cites W2963980460 @default.
- W3204306733 cites W3123015732 @default.
- W3204306733 cites W84912490 @default.
- W3204306733 doi "https://doi.org/10.48550/arxiv.2109.12316" @default.
- W3204306733 hasPublicationYear "2021" @default.
- W3204306733 type Work @default.
- W3204306733 sameAs 3204306733 @default.
- W3204306733 citedByCount "0" @default.
- W3204306733 crossrefType "posted-content" @default.
- W3204306733 hasAuthorship W3204306733A5032538768 @default.
- W3204306733 hasAuthorship W3204306733A5074307078 @default.
- W3204306733 hasAuthorship W3204306733A5090630579 @default.
- W3204306733 hasBestOaLocation W32043067331 @default.
- W3204306733 hasConcept C106159729 @default.
- W3204306733 hasConcept C11413529 @default.
- W3204306733 hasConcept C114614502 @default.
- W3204306733 hasConcept C126255220 @default.
- W3204306733 hasConcept C134306372 @default.
- W3204306733 hasConcept C162324750 @default.
- W3204306733 hasConcept C170131372 @default.
- W3204306733 hasConcept C18903297 @default.
- W3204306733 hasConcept C202615002 @default.
- W3204306733 hasConcept C2777021972 @default.
- W3204306733 hasConcept C2777299769 @default.
- W3204306733 hasConcept C2780009758 @default.
- W3204306733 hasConcept C31010330 @default.
- W3204306733 hasConcept C33923547 @default.
- W3204306733 hasConcept C37914503 @default.
- W3204306733 hasConcept C41008148 @default.
- W3204306733 hasConcept C48103436 @default.
- W3204306733 hasConcept C51955184 @default.
- W3204306733 hasConcept C72134830 @default.
- W3204306733 hasConcept C77088390 @default.
- W3204306733 hasConcept C86803240 @default.
- W3204306733 hasConcept C91575142 @default.
- W3204306733 hasConceptScore W3204306733C106159729 @default.
- W3204306733 hasConceptScore W3204306733C11413529 @default.
- W3204306733 hasConceptScore W3204306733C114614502 @default.
- W3204306733 hasConceptScore W3204306733C126255220 @default.
- W3204306733 hasConceptScore W3204306733C134306372 @default.
- W3204306733 hasConceptScore W3204306733C162324750 @default.
- W3204306733 hasConceptScore W3204306733C170131372 @default.
- W3204306733 hasConceptScore W3204306733C18903297 @default.
- W3204306733 hasConceptScore W3204306733C202615002 @default.
- W3204306733 hasConceptScore W3204306733C2777021972 @default.
- W3204306733 hasConceptScore W3204306733C2777299769 @default.
- W3204306733 hasConceptScore W3204306733C2780009758 @default.
- W3204306733 hasConceptScore W3204306733C31010330 @default.
- W3204306733 hasConceptScore W3204306733C33923547 @default.
- W3204306733 hasConceptScore W3204306733C37914503 @default.
- W3204306733 hasConceptScore W3204306733C41008148 @default.
- W3204306733 hasConceptScore W3204306733C48103436 @default.
- W3204306733 hasConceptScore W3204306733C51955184 @default.
- W3204306733 hasConceptScore W3204306733C72134830 @default.
- W3204306733 hasConceptScore W3204306733C77088390 @default.
- W3204306733 hasConceptScore W3204306733C86803240 @default.
- W3204306733 hasConceptScore W3204306733C91575142 @default.
- W3204306733 hasLocation W32043067331 @default.
- W3204306733 hasOpenAccess W3204306733 @default.
- W3204306733 hasPrimaryLocation W32043067331 @default.
- W3204306733 hasRelatedWork W2007949485 @default.
- W3204306733 hasRelatedWork W2067969086 @default.
- W3204306733 hasRelatedWork W2087092308 @default.
- W3204306733 hasRelatedWork W2593874967 @default.
- W3204306733 hasRelatedWork W2755624257 @default.
- W3204306733 hasRelatedWork W2906105547 @default.
- W3204306733 hasRelatedWork W3034409441 @default.
- W3204306733 hasRelatedWork W3201918700 @default.
- W3204306733 hasRelatedWork W4312599954 @default.
- W3204306733 hasRelatedWork W4379509316 @default.
- W3204306733 isParatext "false" @default.
- W3204306733 isRetracted "false" @default.
- W3204306733 magId "3204306733" @default.
- W3204306733 workType "article" @default.