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Irreversible investment problems

Author

Listed:
  • Anders ûksendal

    (Department of Mathematics, University of Oslo, P.O.Box 1053 Blindern, N-0316 Oslo, Norway Manuscript)

Abstract

This paper mathematically treats the following economic problem: A company wants to expand its capacity in investments that are irreversible. The problem is to find the best investment strategy taking the fluctuating market into account. We give some implicit conditions for a solution in the case where the market process is n-dimensional and an explicit solution in the one dimensional case.

Suggested Citation

  • Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:223-250
    Note: received: May 1998; final version received: June 1999
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    Citations

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    Cited by:

    1. Ferrari, Giorgio & Salminen, Paavo, 2016. "Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary," Center for Mathematical Economics Working Papers 530, Center for Mathematical Economics, Bielefeld University.
    2. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    3. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," LIDAM Discussion Papers CORE 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
    5. 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.
    6. 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.
    7. Torben Koch & Tiziano Vargiolu, 2019. "Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem," Papers 1911.04223, arXiv.org.
    8. Luis H.R. Alvarez E., 2006. "Irreversible Investment, Incremental Capital Accumulation, and Price Uncertainty," Discussion Papers 4, Aboa Centre for Economics.
    9. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 239-271, December.
    10. Alvarez, Luis H.R., 2011. "Optimal capital accumulation under price uncertainty and costly reversibility," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1769-1788, October.
    11. Luis H. R. Alvarez & Erkki Koskela, 2006. "Irreversible Investment under Interest Rate Variability: Some Generalizations," The Journal of Business, University of Chicago Press, vol. 79(2), pages 623-644, March.
    12. Maria B. Chiarolla & Ulrich G. Haussmann, 2005. "Explicit Solution of a Stochastic, Irreversible Investment Problem and Its Moving Threshold," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 91-108, February.
    13. Alain Bensoussan & Benoît Chevalier-Roignant, 2019. "Sequential Capacity Expansion Options," Operations Research, INFORMS, vol. 67(1), pages 33-57, January.
    14. Luis H. R. Alvarez & Erkki Koskela, 2002. "Irreversible Investment under Interest Rate Variability: New Results," CESifo Working Paper Series 640, CESifo.
    15. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    16. Giorgio Ferrari & Paavo Salminen, 2014. "Irreversible Investment under L\'evy Uncertainty: an Equation for the Optimal Boundary," Papers 1411.2395, arXiv.org.
    17. Michal Čermák, 2017. "Leverage Effect and Stochastic Volatility in the Agricultural Commodity Market under the CEV Model," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(5), pages 1671-1678.
    18. Yiannis Kamarianakis & Anastasios Xepapadeas, 2007. "An Irreversible Investment Model with a Stochastic Production Capacity and Fixed Plus Proportional Adjustment Costs," Working Papers 0708, University of Crete, Department of Economics.
    19. Guo, Xin & Pham, Huyên, 2005. "Optimal partially reversible investment with entry decision and general production function," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 705-736, May.
    20. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.

    More about this item

    Keywords

    Optimal stochastic control; irreversible investments; monotone increasing controls; Feller processes;
    All these keywords.

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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