A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians

2021/11/20 by Jackson, Joe, Liang, Gechun · 1 citation
#60H30 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.10597

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.

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• Infinite horizon quadratic backward stochastic differential equations driven by G-Brownian motion

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