Name
Abstract | ||
|---|---|---|
In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form (0.1)dY(t)=−[α1(t)Y(t)+β1(t)Z(t)+∫R0η1(t,ζ)K(t,ζ)ν(dζ)+α2(t)E[Y(t)]+β2(t)E[Z(t)]+∫R0η2(t,ζ)E[K(t,ζ)]ν(dζ)+γ(t)]dt+Z(t)dB(t)+∫R0K(t,ζ)Ñ(dt,dζ),t∈0,T,Y(T)=ξ.where (Y,Z,K) is the unknown solution triplet, B is a Brownian motion, Ñ 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. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.sysconle.2022.105196 | Systems & Control Letters |
Keywords | DocType | Volume |
Mean-field backward stochastic differential equations,Existence and uniqueness,Linear mean-field BSDE,Explicit solution,Mean-field recursive utility problem | Journal | 162 |
ISSN | Citations | PageRank |
0167-6911 | 2 | 0.64 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| N. Agram | 1 | 17 | 3.27 |
| Yaozhong Hu | 2 | 27 | 8.83 |
| Bernt Oksendal | 3 | 89 | 15.84 |