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Explicit investment rules with time-to-build and uncertainty


  • Ren'e Aid
  • Salvatore Federico
  • Huy^en Pham
  • Bertrand Villeneuve


We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpreta- tions for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the in- vestment 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.

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  • Ren'e Aid & Salvatore Federico & Huy^en Pham & Bertrand Villeneuve, 2014. "Explicit investment rules with time-to-build and uncertainty," Papers 1406.0055,
  • Handle: RePEc:arx:papers:1406.0055

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    References listed on IDEAS

    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. 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.
    3. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412,, revised Jan 2015.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-622, June.
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    Cited by:

    1. repec:eee:dyncon:v:82:y:2017:i:c:p:142-164 is not listed on IDEAS
    2. 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.
    3. Julien Prat & Benjamin Walter, 2018. "An Equilibrium Model of the Market for Bitcoin Mining," CESifo Working Paper Series 6865, CESifo Group Munich.
    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. repec:eee:dyncon:v:84:y:2017:i:c:p:1-31 is not listed on IDEAS

    More about this item

    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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