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Analytical solution to an investment problem under uncertainties with shocks

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  • Cl'audia Nunes
  • Rita Pimentel

Abstract

We derive the optimal investment decision in a project where both demand and investment costs are stochastic processes, eventually subject to shocks. We extend the approach used in Dixit and Pindyck (1994), chapter 6.5, to deal with two sources of uncertainty, but assuming that the underlying processes are no longer geometric Brownian diffusions but rather jump diffusion processes. For the class of isoelastic functions that we address in this paper, it is still possible to derive a closed expression for the value of the firm. We prove formally that the result we get is indeed the solution of the optimization problem.

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  • Cl'audia Nunes & Rita Pimentel, 2015. "Analytical solution to an investment problem under uncertainties with shocks," Papers 1509.04135, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1509.04135
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    References listed on IDEAS

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    1. Martzoukos, Spiros H. & Trigeorgis, Lenos, 2002. "Real (investment) options with multiple sources of rare events," European Journal of Operational Research, Elsevier, vol. 136(3), pages 696-706, February.
    2. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    3. Wu, Liang-Chuan & Li, Shu-Hsing & Ong, Chorng-Shyong & Pan, Chungteh, 2012. "Options in technology investment games: The real world TFT-LCD industry case," Technological Forecasting and Social Change, Elsevier, vol. 79(7), pages 1241-1253.
    4. Hagspiel, Verena & Huisman, Kuno J.M. & Nunes, Clàudia, 2015. "Optimal technology adoption when the arrival rate of new technologies changes," European Journal of Operational Research, Elsevier, vol. 243(3), pages 897-911.
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