Existence of relaxed optimal control for $G$-neutral stochastic functional differential equations with uncontrolled diffusion
Vol. 17 No. 2 (2022) P.143~P.172
DOI: || https://doi.org/10.21915/BIMAS.2022202 |
| ||10.21915/BIMAS.2022202 |
In this paper, we study under refined Lipschitz hypothesis, the question of existence
and uniqueness of solution of controlled neutral stochastic functional differential equations
driven by $G$-Brownian motion ($G$-NSFDEs in short). An existence of a relaxed optimal
control where the neutral and diffusion terms do not depend on the control variable was the
main result of the article. The latter is done by using tightness techniques and the weak
convergence techniques for each probability measure in the set of all possible probabilities
of our dynamic. A motivation of our work is presented and a numerical analysis for the
uncontrolled $G$-NSFDE is given.
$G$-neutral stochastic functional differential equations, $G$-expectation, $G$-Brownian motion, $G$-optimal relaxed control, numerical analysis.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 93E20, 60H07, 60H10, 60H30
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