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

Abstract

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.

Keywords:

• real-asset martingale valuation
• optimum inventory control
• newsvendor model
• market-based approach
• jumps with stochastic volatility and intensity
• forward commitments