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Explicit investment rules with time-to-build and uncertainty

Author

Listed:
  • René Aid

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine)

  • Salvatore Federico

    () (Dipartimento di Economia, Management e Metodi Quantitativi, Universitá di Milano - Department of Economics, Business and Statistics - Università degli studi di Milano [Milano])

  • Huyen Pham

    () (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Villeneuve

    (LEDA - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique - FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine - LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine)

Abstract

We establish explicit socially optimal rules for an irreversible investment decision with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpretations for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the investment in the pipeline, must never drop below the best predictor of future demand, minus two biases. The discounting bias takes into account the fact that investment is paid upfront for future use; the precautionary bias multiplies a type of risk aversion index by the local volatility. Relying on the analytical forms, we discuss in detail the economic effects.

Suggested Citation

  • René Aid & Salvatore Federico & Huyen Pham & Bertrand Villeneuve, 2014. "Explicit investment rules with time-to-build and uncertainty," Working Papers hal-00997994, HAL.
  • Handle: RePEc:hal:wpaper:hal-00997994
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00997994
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    References listed on IDEAS

    as
    1. Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
    2. Pacheco-de-Almeida, Goncalo & Zemsky, Peter, 2003. " The Effect of Time-to-Build on Strategic Investment under Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 166-182, Spring.
    3. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-622, June.
    4. Felipe L. Aguerrevere, 2003. "Equilibrium Investment Strategies and Output Price Behavior: A Real-Options Approach," Review of Financial Studies, Society for Financial Studies, vol. 16(4), pages 1239-1272.
    5. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
    6. Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
    7. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    8. Milne, Alistair & Whalley, A Elizabeth, 2000. "'Time to build, option value and investment decisions': a comment," Journal of Financial Economics, Elsevier, vol. 56(2), pages 325-332, May.
    9. Bruder, Benjamin & Pham, Huyên, 2009. "Impulse control problem on finite horizon with execution delay," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1436-1469, May.
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    Cited by:

    1. Julien Prat & Benjamin Walter, 2018. "An Equilibrium Model of the Market for Bitcoin Mining," CESifo Working Paper Series 6865, CESifo Group Munich.
    2. repec:eee:dyncon:v:82:y:2017:i:c:p:142-164 is not listed on IDEAS
    3. repec:eee:dyncon:v:84:y:2017:i:c:p:1-31 is not listed on IDEAS
    4. Julien Prat & Walter Benjamin, 2017. "An Equilibrium Model of the Market for Bitcoin Mining," Working Papers 2017-15, Center for Research in Economics and Statistics.
    5. Genc, Talat S., 2017. "The impact of lead time on capital investments," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 142-164.

    More about this item

    Keywords

    delay equations; optimal capacity; irreversible investments; singular stochastic control; time-to-build; delay equations.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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