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

Jack SK Chang, Carolyn Chang and Min Shi
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Jack SK Chang: Department of Finance and Law, California State University, Los Angeles, USA
Carolyn Chang: Department of Finance, California State University, Fullerton, USA
Min Shi: Department of Management, California State University, Los Angeles, USA

Journal of the Operational Research Society, 2015, vol. 66, issue 3, 405-420

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.

Date: 2015
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