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A new approach to solve the continuous-time stochastic inventory problemusing the fluctuation theory of Levy processes is developed. This approachinvolves the recent developments of the scale function that is capable ofexpressing many fluctuation identities of spectrally one-sided Levy processes.For the case with a fixed cost and a general spectrally positive Levy demandprocess, we show the optimality of an (s,S)-policy. The optimal policy and thevalue function are concisely expressed via the scale function. Numericalexamples under a Levy process in the beta-family with jumps of infiniteactivity are provided to confirm the analytical results. Furthermore, the casewith no fixed ordering costs is studied.

Inventory Control for Spectrally Positive Levy Demand Processes