A constructive approach to existence of equilibria in time-inconsistent stochastic control problems
Optimization and Control
2021-10-01 v2 Probability
Abstract
We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach relies on a time discretization of the control problem via n-person games, which are characterized via the maximum principle using Backward Stochastic Differential Equations (BSDEs). The existence of equilibria is proved by applying weak convergence arguments to the solutions of n-person games. A numerical implementation is provided by approximating n-person games using finite Markov chains.
Cite
@article{arxiv.2104.14334,
title = {A constructive approach to existence of equilibria in time-inconsistent stochastic control problems},
author = {Jiang Yu Nguwi and Nicolas Privault},
journal= {arXiv preprint arXiv:2104.14334},
year = {2021}
}