Affiliation:
1. Laboratory of Applied Mathematics , Mohamed Khider University , P. O. Box 145 , Biskra 07000 , Algeria
Abstract
Abstract
We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter
H
∈
(
0
,
1
)
{H\in(0,1)}
, in the case where the set of the control domain is convex. We provide an estimation of the solution and establish the necessary and sufficient optimality conditions in the form of the stochastic maximum principle.
We apply the theory to solve a linear quadratic stochastic control problem.
Reference19 articles.
1. C. Bender,
Explicit solutions of a class of linear fractional BSDEs,
Systems Control Lett. 54 (2005), 671–680.
2. F. Biagini, Y. Hu, B. Øksendal and A. Sulem,
A stochastic maximum principle for processes driven by fractional Brownian motion,
Stochastic Process. Appl. 100 (2002), 233–253.
3. F. Biagini, Y. Hu, B. Øksendal and T. Zhang,
Stochastic Calculus for Fractional Brownian Motion and Applications,
Probab. Appl. (New York),
Springer, London, 2008.
4. T. Bouaziz and A. Chala,
Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application,
Random Oper. Stoch. Equ. 28 (2020), no. 4, 291–306.
5. T. Bouaziz and A. Chala,
Pontryagin’s risk-sensitive SMP for fractional BSDEs via Malliavin calculus,
J. Appl. Probab. Stat. 17 (2022), 141–160.