Singular Control in Inventory Management with Smooth Ambiguity
Arnon Archankul, Jacco J.J. Thijssen

TL;DR
This paper develops a framework for singular inventory control under smooth ambiguity, integrating robust utility, stochastic filtering, and numerical methods to analyze optimal policies and the impact of ambiguity on decision timing.
Contribution
It introduces a novel approach to singular control under smooth ambiguity, linking it with Kalman-Bucy filtering and providing a numerical scheme for implementation.
Findings
Ambiguity causes earlier action and reduces the continuation region.
The continuation region is divided into target, learning, and control zones.
Longer learning periods increase confidence and influence control decisions.
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. Additionally, we prove that the cost function can be determined by solving forward-backward stochastic differential equations with quadratic growth. With a sufficient condition and utilising variational inequalities in a viscosity sense, we derive the value function and optimal control policy. By the change-of-coordinate technique, we transform the problem into two-dimensional singular control, offering insights into model learning and aligning with classical singular control free boundary problems. We numerically implement our theory using a Markov chain approximation, where inventory…
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Taxonomy
TopicsSupply Chain and Inventory Management · Stochastic processes and financial applications · Advanced Queuing Theory Analysis
