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Explicit investment rules with time to built and uncertainty

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Date
2015
Dewey
Théorie économique
Sujet
Optimal capacity; Irreversible investments; Singular stochastic control; Time-to-build; Delay equations
JEL code
E.E2.E22; D.D9.D92; C.C6.C61
Journal issue
Journal of Economic Dynamics & Control
Volume
51
Publication date
2015
Article pages
240-256
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jedc.2014.10.010
URI
https://basepub.dauphine.fr/handle/123456789/19893
Collections
  • LEDa : Publications
Metadata
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Author
Aïd, René
163511 Laboratoire d'Economie de Dauphine [LEDa]
Federico, Salvatore
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Pham, Huyên
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Villeneuve, Bertrand
163511 Laboratoire d'Economie de Dauphine [LEDa]
Type
Article accepté pour publication ou publié
Abstract (EN)
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. For example, the impact of volatility on the optimal investment is negligible in some cases. It vanishes in the CIR model for long delays, and in the GBM model for high discount rates.

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