Robust Ergodic Control of Jump–Diffusion Systems with Drift and Intensity Uncertainty

A. Guada Azze, B. D'Auria, G. Ferrari

We study a long-run regulation problem for a jump-diffusion subject to continuous fluctuations and compound Poisson shocks, with ambiguity in both drift and jump intensity. A decision maker uses upward and downward singular controls to keep the system within desirable levels, while model uncertainty is captured through entropy-penalized distortions, yielding a robust max-min ergodic singular control problem. We characterize the optimal policy through the associated HJB equation, a nonlinear integro-differential free-boundary problem. The worst-case parameters have a bang-bang form, and the optimal regulation policy is of reflecting-barrier type. For exponentially distributed jumps, the problem reduces to linear ODEs, enabling stable numerical computation of optimal barriers and the ergodic value. Comparative statics show that ambiguity and model parameters significantly reshape the optimal inaction region and typically induce more cautious regulation.

Keywords: robust control, singular stochastic control, jump--diffusion, ergodic control, model uncertainty, free-boundary problems

Stochastic Processes
September 2, 2026  5:40 PM
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