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Mean-field backward stochastic differential equations and applications
Linnaeus University, Faculty of Technology, Department of Mathematics. University Med Khider, Algeria. (Stochastic analysis and stochastic processes)
University of Alberta, Canada;University of Oslo, Norway.
University of Oslo, Norway.
(English)In: Article in journal (Refereed) Submitted
Abstract

In this paper we study the mean-field backward stochastic differential equations (mean-field bsde) of the form

dY (t) = −f(t, Y (t), Z(t), K(t, ·), E[ϕ(Y (t), Z(t), K(t, ·))])dt + Z(t)dB(t) + R R0 K(t, ζ)N˜(dt, dζ),

where B is a Brownian motion, N˜ is the compensated Poisson random measure. Under some mild conditions, we prove the existence and uniqueness of the solution triplet (Y, Z, K). It is commonly believed that there is no comparison theorem for general mean-field bsde. However, we prove a comparison theorem for a subclass of these equations.When the mean-field bsde is linear, we give an explicit formula for the first component Y (t) of the solution triplet. Our results are applied to solve a mean-field recursive utility optimization problem in finance.

National Category
Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-82307OAI: oai:DiVA.org:lnu-82307DiVA, id: diva2:1307469
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-08-28

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CiteExportLink to record
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Citation style
  • apa
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  • Other locale
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