Explicit Investment Rules with Time-to-Build and Uncertainty

22 Pages Posted: 25 Jun 2014 Last revised: 9 May 2017

See all articles by René Aïd

René Aïd

Université Paris-Dauphine

Salvatore Federico

University of Milan

Huyên Pham

Université Paris VII Denis Diderot

Bertrand Villeneuve

Université Paris-Dauphine, PSL Research University

Date Written: October 17, 2014

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. 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.

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

JEL Classification: C61; E92; D22

Suggested Citation

Aid, Rene and Federico, Salvatore and Pham, Huyen and Villeneuve, Bertrand, Explicit Investment Rules with Time-to-Build and Uncertainty (October 17, 2014). Journal of Economic Dynamics and Control, Vol. 51, pp. 240-256, 2015 . Available at SSRN: https://ssrn.com/abstract=2458499 or http://dx.doi.org/10.2139/ssrn.2458499

Rene Aid

Université Paris-Dauphine ( email )

Place du Maréchal de Lattre de Tassigny
Paris, 75016
France

Salvatore Federico

University of Milan ( email )

Via Festa del Perdono, 7
Milan, 20122
Italy

Huyen Pham

Université Paris VII Denis Diderot ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205
France

Bertrand Villeneuve (Contact Author)

Université Paris-Dauphine, PSL Research University ( email )

Place du Maréchal de Lattre de Tassigny
Paris, 75016
France

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