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Mean-field backward stochastic differential equations and applications
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-1662-0215
Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
2022 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, article id 105196Article in journal (Refereed) Published
Abstract [en]

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

Place, publisher, year, edition, pages
Elsevier BV , 2022. Vol. 162, article id 105196
Keywords [en]

Mean-field backward stochastic differential equations

, Existence and uniqueness, Linear mean-field BSDE, Explicit solution, Mean-field recursive utility problem
National Category
Probability Theory and Statistics Mathematical Analysis Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-312195DOI: 10.1016/j.sysconle.2022.105196ISI: 000788749000012Scopus ID: 2-s2.0-85126959192OAI: oai:DiVA.org:kth-312195DiVA, id: diva2:1658830
Note

QC 20220518

Available from: 2022-05-18 Created: 2022-05-18 Last updated: 2022-06-25Bibliographically approved

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Agram, Nacira

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