A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy |
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Authors: | Jack SK Chang Carolyn Chang Min Shi |
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Affiliation: | 1.Department of Finance and Law,California State University,Los Angeles,USA;2.Department of Finance,California State University,Fullerton,USA;3.Department of Management,California State University,Los Angeles,USA |
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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. |
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