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Irreversible investment problems


  • Anders ûksendal

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


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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    References listed on IDEAS

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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. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," CORE Discussion Papers 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412,, revised Jan 2015.
    4. Luis H. R. Alvarez & Erkki Koskela, 2002. "Irreversible Investment under Interest Rate Variability: New Results," CESifo Working Paper Series 640, CESifo Group Munich.
    5. 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.
    6. Giorgio Ferrari & Paavo Salminen, 2014. "Irreversible Investment under L\'evy Uncertainty: an Equation for the Optimal Boundary," Papers 1411.2395,
    7. 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.
    8. Luis H.R. Alvarez E., 2006. "Irreversible Investment, Incremental Capital Accumulation, and Price Uncertainty," Discussion Papers 4, Aboa Centre for Economics.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.

    More about this item


    Optimal stochastic control; irreversible investments; monotone increasing controls; Feller processes;

    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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