Here, there and everywhere: state-dependent time-inconsistent stochastic control
Optimization and Control
2026-03-24 v1 Theoretical Economics
Probability
Mathematical Finance
Abstract
This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate the equilibrium value function essential for resolving cases where the present state affecting the target functional triggers the inconsistency. Additionally, the paper offers an application exemplifying this theory through the time-inconsistent linear--quadratic regulator.
Cite
@article{arxiv.2603.22022,
title = {Here, there and everywhere: state-dependent time-inconsistent stochastic control},
author = {Dylan Possamaï and Mateo Rodriguez Polo},
journal= {arXiv preprint arXiv:2603.22022},
year = {2026}
}
Comments
39 pages, 2 figures