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On an optimal extraction problem with regime switching

Author

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  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Yang, Shuzhen

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper studies an optimal irreversible extraction problem of an exhaustible commodity in presence of regime shifts. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian motion with volatility modulated by a two state Markov chain. In this setting, the company aims at finding the extraction rule that maximizes its expected, discounted net cash flow. The problem is set up as a finite-fuel two-dimensional degenerate singular stochastic control problem over an infinite time-horizon. We provide explicit expressions both for the value function and for the optimal control. We show that the latter prescribes a Skorokhod reflection of the optimally controlled state process at a certain state and price dependent threshold. This curve is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching. The techniques are those of stochastic calculus and stochastic optimal control theory.

Suggested Citation

  • Ferrari, Giorgio & Yang, Shuzhen, 2016. "On an optimal extraction problem with regime switching," Center for Mathematical Economics Working Papers 562, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:562
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    File URL: https://pub.uni-bielefeld.de/download/2904731/2904732
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    References listed on IDEAS

    as
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    7. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2014. "A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries," Papers 1405.2442, arXiv.org, revised Nov 2014.
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    11. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
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