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A generalized complementarity approach to solving real option problems

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  • Nagae, Takeshi
  • Akamatsu, Takashi

Abstract

This article provides a unified framework for analyzing a wide variety of real option problems. These problems include the frequently studied, simple real option problems, as described in Dixit and Pindyck [1994. Investment Under Uncertainty. Princeton University Press, Princeton] for example, but also problems with more complicated and realistic assumptions. We reveal that all the real option problems belonging to the more general class considered in this study are described by the same mathematical structure, which can be solved by applying a computational algorithm developed in the field of mathematical programming. More specifically, all of the present real option problems can be directly solved by reformulating their optimality condition as a dynamical system of generalized linear complementarity problems (GLCPs). This enables us to develop an efficient and robust algorithm for solving a broad range of real option problems in a unified manner, exploiting recent advances in the theory of complementarity problems.

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  • Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.
    • Handle: RePEc:eee:dyncon:v:32:y:2008:i:6:p:1754-1779
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    3. Gamba, Andrea & Tesser, Matteo, 2009. "Structural estimation of real options models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 798-816, April.
    4. Ali Naef Mohammad, 2016. "Valuation Tools for Determining the Value of Assets: A Literature Review," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 6(4), pages 63-72, October.
    5. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    6. Akamatsu, Takashi & Nagae, Takeshi, 2011. "A network of options: Evaluating complex interdependent decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 714-729, May.
    7. A. Mantovi, 2009. "Long run value stabilization in a real options perspective," Economics Department Working Papers 2009-EP01, Department of Economics, Parma University (Italy).
    8. Francesco Mezzadri & Emanuele Galligani, 2022. "Projected Splitting Methods for Vertical Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 598-620, June.

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