A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians
Abstract
We establish the existence (and in an appropriate sense uniqueness) of Markovian solutions for ergodic BSDEs under a novel monotonicity condition. Our monotonicity condition allows us to prove existence even when the driver f has arbitrary (in particular super-quadratic) growth in z, which reveals an interesting trade-off between monotonicity and growth for ergodic BSDEs. The technique of proof is to establish a probabilistic representation of the derivative of the Markovian solution, and then use this representation to obtain a-priori estimates. Our study is motivated by applications to ergodic control, and we use our existence result to prove the existence of optimal controls for a class of ergodic control problems with potentially super-quadratic Hamiltonians. We also treat a class of drivers coming from the construction of forward performance processes, and interpret our monotonicity condition in this setting.
Keywords
Cite
@article{arxiv.2111.10597,
title = {A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians},
author = {Joe Jackson and Gechun Liang},
journal= {arXiv preprint arXiv:2111.10597},
year = {2022}
}