Relaxed Optimal Control Problem for a Finite Horizon G-SDE with Delay and Its Application in Economics
Optimization and Control
2023-08-29 v2 Probability
Abstract
This paper investigates the existence of a G-relaxed optimal control of a controlled stochastic differential delay equation driven by G-Brownian motion (G-SDDE in short). First, we show that optimal control of G-SDDE exists for the finite horizon case. We present as an application of our result an economic model, which is represented by a G-SDDE, where we studied the optimization of this model. We connected the corresponding Hamilton Jacobi Bellman equation of our controlled system to a decoupled G-forward backward stochastic differential delay equation (G-FBSDDE in short). Finally, we simulate this G-FBSDDE to get the optimal strategy and cost.
Keywords
Cite
@article{arxiv.2303.17427,
title = {Relaxed Optimal Control Problem for a Finite Horizon G-SDE with Delay and Its Application in Economics},
author = {Omar Kebiri and Nabil Elgroud},
journal= {arXiv preprint arXiv:2303.17427},
year = {2023}
}