A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy

We propose a novel market‐based approach to optimum inventory control in a doubly stochastic jump‐diffusion economy by modelling a commodity distributor’s inventory investment as a portfolio of forward commitments with explicit accounting of the jump‐diffusion dynamics of demands, costs, and prices in open markets. We apply the robust real‐asset martingale valuation methodology to derive a closed‐form solution for the inventory value and a simple and intuitive optimality condition. Numerical analysis verifies this condition and demonstrates that the resulting optimum policy has robust properties in relation to the stylized effects.