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Optimality of doubly reflected Lévy processes in singular control

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  • Baurdoux, Erik J.
  • Yamazaki, Kazutoshi

Abstract

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Lévy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Lévy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results.

Suggested Citation

  • Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:61617
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    Cited by:

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    3. Noba, Kei, 2021. "On the optimality of double barrier strategies for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 73-102.

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    More about this item

    Keywords

    Singular control; Doubly reflected Lévy processes; Fluctuation theory; Scale functions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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