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There is ample evidence that the demand for products held in an inventory system is often correlated with the returns of securities in financial markets. Therefore, the risks associated with the profit or cash flow in the inventory system can be hedged by investing in a portfolio of instruments in the financial system. In order to get insights, we take this idea to the extreme by supposing that random demand, as well as random supply, both depend “perfectly” on the price of a security in an almost arbitrary fashion. This allows one to represent the cash flow by a replicating portfolio of derivative securities and bonds. Thus, the value of the cash flow needs to be determined in terms of the prices of these financial instruments. The decisions of the inventory manager are therefore based on this pricing mechanism. In particular, in a complete market with some risk-neutral martingale measure that yields no arbitrage opportunities, the expected value of the cash flow should be determined using this measure. We discuss these issues in the context of a single period newsvendor model with random demand and supply.
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