Search: id:"swepub:oai:DiVA.org:kth-312195" >
Mean-field backward...
Mean-field backward stochastic differential equations and applications
-
- Agram, Nacira (author)
- KTH,Matematik (Inst.)
-
- Hu, Yaozhong (author)
- Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
-
- oksendal, Bernt (author)
- Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway.
-
KTH Matematik (Inst) (creator_code:org_t)
- Elsevier BV, 2022
- 2022
- English.
-
In: Systems & control letters (Print). - : Elsevier BV. - 0167-6911 .- 1872-7956. ; 162
- Related links:
-
https://doi.org/10.1...
-
show more...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
show less...
Abstract
Subject headings
Close
- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Annan matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Other Mathematics (hsv//eng)
Keyword
- <p>Mean-field backward stochastic differential equations</p>
- Existence and uniqueness
- Linear mean-field BSDE
- Explicit solution
- Mean-field recursive utility problem
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
To the university's database