Abstract
We consider the classical single commodity newsvendor inventory management problem in a stochastic setup, where the distribution of the commodity price satisfies martingale and marginal constraints implied by no–arbitrage arguments. We demonstrate a strong duality between the newsvendor’s optimization problem and the canonical martingale Schrödinger bridge (Schrödinger, 1932 ), which is the entropy minimizing martingale coupling amongst all equivalent martingale couplings of marginal distributions of the ex–ante and ex–post spot prices. We obtain primal and dual attainment results under mild restrictions on the physical probability measure. We also characterize vendor’s optimal inventory policy in terms of its dual martingale Schrödinger bridge.