Ergodic BSDEs with jumps and time dependence

Abstract

In this paper we look at ergodic BSDEs in the case where the forward dynamics are given by the solution to a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck SDE with Lévy noise, taking values in a separable Hilbert space. We establish the existence of a unique bounded solution to an infinite horizon discounted BSDE. We then use the vanishing discount approach, together with coupling techniques, to obtain a Markovian solution to the EBSDE. We also prove uniqueness under certain growth conditions. Applications are then given, in particular to risk-averse ergodic optimal control and power plant evaluation under uncertainty.

References in corpus (1)

• Exponential ergodicity and regularity for equations with Lévy noise

Cited by in corpus (2)

• Ergodic BSDEs driven by G-Brownian motion and their applications
• Classical Adjoints for Ergodic Stochastic Control