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.
| Subjects: | Optimization and Control (math.OC); Probability (math.PR) |
| MSC classes: | 93E20, 49L20, 60J75, 90C40 |
| Cite as: | arXiv:2605.24646 [math.OC] |
| (or arXiv:2605.24646v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24646 arXiv-issued DOI via DataCite (pending registration) |
From: Abel Azze [view email]
[v1]
Sat, 23 May 2026 16:27:16 UTC (2,146 KB)
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