Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty
Abstract
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in applications including inventory control, cash management, and capacity planning. We formulate the problem as a robust ergodic singular control problem in which a decision maker applies upward and downward interventions while accounting for model ambiguity through entropy-penalized distortions. The resulting max-min problem involves a long-run average performance criterion. We show that the associated Hamilton--Jacobi--Bellman equation reduces to a nonlinear integro-differential free-boundary problem with a tractable structure. The worst-case model exhibits a bang-bang form, and the optimal policy is characterized by reflecting barriers. Under exponentially distributed jumps, the problem further reduces to a system of ordinary differential equations, enabling efficient numerical computation.
Cite
@article{arxiv.2605.24646,
title = {Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty},
author = {Abel Azze and Bernardo D'Auria and Giorgio Ferrari},
journal= {arXiv preprint arXiv:2605.24646},
year = {2026}
}