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Stochastic optimal control of McKean-Vlasov equations with anticipating law
Linnaeus University, Faculty of Technology, Department of Mathematics. (Stochastic analysis and stochastic processes)
2019 (English)In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 30, no 5-6, p. 879-901Article in journal (Refereed) Published
Abstract [en]

We are interested in Pontryagin’s stochastic maximum principle of controlled McKean–Vlasov stochastic differential equations. We allow the law to be anticipating, in the sense that, the coefficients (the drift and the diffusion coefficients) depend not only of the solution at the current time t, but also on the law of the future values of the solution PX(t+δ)" role="presentation">PX(t+δ), for a given positive constant δ" role="presentation">δ. We emphasise that being anticipating w.r.t. the law of the solution process does not mean being anticipative in the sense that it anticipates the driving Brownian motion. As an adjoint equation, a new type of delayed backward stochastic differential equations (BSDE) with implicit terminal condition is obtained. By using that the expectation of any random variable is a function of its law, our BSDE can be written in a simple form. Then, we prove existence and uniqueness of the solution of the delayed BSDE with implicit terminal value, i.e. with terminal value being a function of the law of the solution itself.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 30, no 5-6, p. 879-901
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-82298DOI: 10.1007/s13370-019-00689-wOAI: oai:DiVA.org:lnu-82298DiVA, id: diva2:1307456
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-08-28Bibliographically approved

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Agram, Nacira

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CiteExportLink to record
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  • apa
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
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