Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty
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| Format: | Preprint |
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2026
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| _version_ | 1866913159342718976 |
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| author | Azze, Abel D'Auria, Bernardo Ferrari, Giorgio |
| author_facet | Azze, Abel D'Auria, Bernardo Ferrari, Giorgio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_24646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty Azze, Abel D'Auria, Bernardo Ferrari, Giorgio Optimization and Control Probability 93E20, 49L20, 60J75, 90C40 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. |
| title | Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty |
| topic | Optimization and Control Probability 93E20, 49L20, 60J75, 90C40 |
| url | https://arxiv.org/abs/2605.24646 |