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Singular Control Optimal Stopping of Memory Mean-Field Processes
Univ Oslo, Dept Math, Oslo, Norway.
Univ Oslo, Dept Math, Oslo, Norway.
Univ Oslo, Dept Math, Oslo, Norway.
2019 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, Vol. 51, no 1, p. 450-568Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward stochastic differential equations; and (iii) optimal stopping of mean-field stochastic differential equations. More specifically, we do the following: (1) We prove the existence and uniqueness of the solutions of some reflected advanced memory backward stochastic differential equations; (2) we give sufficient and necessary conditions for an optimal singular control of a memory mean-field stochastic differential equation (MMSDE) with partial information; and (3) we deduce a relation between the optimal singular control of an MMSDE and the optimal stopping of such processes.

Place, publisher, year, edition, pages
2019. Vol. 51, no 1, p. 450-568
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-52820DOI: 10.1137/18M1174787ISI: 000459957700018Scopus ID: 2-s2.0-85063068181OAI: oai:DiVA.org:mdh-52820DiVA, id: diva2:1510255
Available from: 2020-12-15 Created: 2020-12-15 Last updated: 2021-02-16Bibliographically approved

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Bachouch, Achref

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