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Irreversible investment with fixed adjustment costs: a stochastic impulse control approach

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  • Salvatore Federico
  • Mauro Rosestolato
  • Elisa Tacconi

Abstract

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.

Suggested Citation

  • Salvatore Federico & Mauro Rosestolato & Elisa Tacconi, 2018. "Irreversible investment with fixed adjustment costs: a stochastic impulse control approach," Papers 1801.04491, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1801.04491
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    References listed on IDEAS

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    1. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "Optimal Boundary Surface for Irreversible Investment with Stochastic Costs," Papers 1406.4297, arXiv.org, revised Jan 2017.
    2. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2017. "Optimal Boundary Surface for Irreversible Investment with Stochastic Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1135-1161, November.
    3. Aïd, René & Federico, Salvatore & Pham, Huyên & Villeneuve, Bertrand, 2015. "Explicit investment rules with time-to-build and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 240-256.
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    7. Luis Alvarez, 2010. "Irreversible capital accumulation under interest rate uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 249-271, October.
    8. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    9. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
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    11. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
    12. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
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    Cited by:

    1. Huberts, Nick F.D. & Rossi Silveira, Rafael, 2023. "How economic depreciation shapes the relationship of uncertainty with investments’ size & timing," International Journal of Production Economics, Elsevier, vol. 260(C).
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    3. Francesco Giuseppe Cordoni & Luca Di Persio & Yilun Jiang, 2020. "A Bank Salvage Model by Impulse Stochastic Controls," Risks, MDPI, vol. 8(2), pages 1-31, June.
    4. Torben Koch & Tiziano Vargiolu, 2019. "Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem," Papers 1911.04223, arXiv.org.
    5. Junkee Jeon & Geonwoo Kim, 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon," Mathematics, MDPI, vol. 8(11), pages 1-10, November.

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