Inventory Control for Spectrally Positive Levy Demand Processes
arXiv:1303.5163
Abstract
A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many fluctuation identities of spectrally one-sided Levy processes. For the case with a fixed cost and a general spectrally positive Levy demand process, we show the optimality of an (s,S)-policy. The optimal policy and the value function are concisely expressed via the scale function. Numerical examples under a Levy process in the beta-family with jumps of infinite activity are provided to confirm the analytical results. Furthermore, the case with no fixed ordering costs is studied.
Final version. To appear in Mathematics of Operations Research
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Cited by in corpus (6)
- Contraction options and optimal multiple-stopping in spectrally negative Levy models
- Optimality of doubly reflected Levy processes in singular control
- Optimality of Refraction Strategies for Spectrally Negative Levy Processes
- Cash Management and Control Band Policies for Spectrally One-sided Levy Processes
- Games of singular control and stopping driven by spectrally one-sided Levy processes
- Optimal dividends in the dual model under transaction costs