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Ergodic BSDEs with jumps and time dependence
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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 L\'evy 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.
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Path-Dependent Ergodic Optimal Control and Backward Stochastic Differential Equations
Establishes well-posedness, verification and stability for a new class of path-dependent infinite-horizon ergodic BSDEs on unbounded domains under extended dissipativity, with the ergodic cost characterized by asympto...
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