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Mean-field stochastic control with elephant memory in finite and infinite time horizon
Linnaeus University, Faculty of Technology, Department of Mathematics. Univ Oslo, Norway.
Univ Oslo, Norway.
2019 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516Article in journal (Refereed) Epub ahead of print
Abstract [en]

Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case. In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem. For infinite horizon, we derive sufficient and necessary maximum principles. As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2019.
Keywords [en]
Mean-field stochastic differential equation, memory, stochastic maximum principle, partial information, backward stochastic differential equation
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-87061DOI: 10.1080/17442508.2019.1635600ISI: 000476441900001OAI: oai:DiVA.org:lnu-87061DiVA, id: diva2:1339955
Available from: 2019-08-01 Created: 2019-08-01 Last updated: 2019-09-26

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Agram, Nacira

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  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf