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1075. Singular Control in Inventory Management with Smooth Ambiguity
Invited abstract in session MB-33: Dynamics of the Firm I, stream Optimal Control Theory and Applications.
Monday, 10:30-12:00Room: 42 (building: 303A)
Authors (first author is the speaker)
| 1. | Arnon Archankul
|
| Department of Mathematics, University of York | |
| 2. | Jacco Thijssen
|
| Management School & Department of Mathematics, University of York |
Abstract
We consider singular control in inventory management under Knightian uncertainty, where decision-makers have a smooth ambiguity preference over Gaussian-generated priors. We demonstrate that continuous-time smooth ambiguity is the infinitesimal limit of Kalman-Bucy filtering with recursive robust utility, heuristically proposed by Hansen and Sargent (Journal of Economic Theory, 146(3):1195–1223, 2011). Additionally, we prove that the cost function can be determined by solving forward-backward stochastic differential equations with quadratic growth. Using variational inequalities in a viscosity sense, we derive the value function and optimal control policy. By a coordinated transformation, we simplify the problem into two-dimensional singular control, offering insights into model learning and aligning with classical singular control free boundary problems. This study marks the first attempt, to our knowledge, to integrate singular control with smooth ambiguity.
Keywords
- Inventory
- Decision Analysis
- Robust Optimization
Status: accepted
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