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Mean-field backward stochastic differential equations and applications
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).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 (engelsk)Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, artikkel-id 105196Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Elsevier BV , 2022. Vol. 162, artikkel-id 105196
Emneord [en]

Mean-field backward stochastic differential equations

, Existence and uniqueness, Linear mean-field BSDE, Explicit solution, Mean-field recursive utility problem
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Identifikatorer
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
Merknad

QC 20220518

Tilgjengelig fra: 2022-05-18 Laget: 2022-05-18 Sist oppdatert: 2022-06-25bibliografisk kontrollert

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