Explicit investment rules with time-to-build and uncertainty |
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Affiliation: | 1. EDF R&D, France;2. Università degli Studi di Milano, Italy;3. LPMA, Université Paris-Diderot, France;4. LEDa, Université Paris-Dauphine, France;1. Newcastle University Business School, 5 Barrack Road, Newcastle upon Tyne NE1 4SE, UK;2. CeNDEF, Amsterdam School of Economics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands;1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China;2. Institute of Mathematics, Shandong University, Jinan 250100, China |
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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. |
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Keywords: | Optimal capacity Irreversible investments Singular stochastic control Time-to-build Delay equations |
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