Opções reais sob Incerteza Knightiana na avaliação econômica de projetos de Pesquisa e Desenvolvimento (P&D)
Real Options under Knightian Uncertainty for Economic Evaluation of Research and Development (R&D) Projects
Leite, Luís Alberto Melchíades; Santiago, Leonardo Pereira; Teixeira, José Paulo
http://dx.doi.org/10.1590/0103-6513.009611
Production, vol.25, n3, p.641-656, 2015
Resumo
Este trabalho incorpora tratamento quantitativo da incerteza, no sentido da definição clássica de Frank Knight (1921), a um modelo de avaliação econômica baseado em Opções Reais, analisando suas consequências. O conceito knightiano distingue incerteza de risco. Decisões ótimas indicadas pelo Modelo de Opções Reais, uma vez não seguidas pelos decisores, tornam-se escolhas subótimas, sugerindo a presença de elementos de Incerteza Knightiana no ambiente decisório. Decisões subótimas contrariam a regra básica do VPL e, sendo o decisor racional por premissa, existe uma espécie de VPL ex post que se harmoniza à escolha, adequando-se à regra decisória e determinando quantitativamente um grau de aversão à incerteza no decisor. Introduzindo-se no modelo o Valor Esperado de Choquet e um parâmetro representando aversão à incerteza, sob o conceito de probabilidades não aditivas, obtêm-se aproximações de VPLs pós-decisão e graus de aversão à incerteza revelados. A formulação proposta é aplicada em avaliação de projeto de P&D.
Palavras-chave
Decisão sob incerteza. Opções Reais em P&D. Avaliação econômica de projetos. P&D incremental. Incerteza Knightiana.
Abstract
This article presents a quantitative treatment of uncertainty, in the classical sense of Frank Knight (1921), in an economic assessment model that is based on Real Options Theory. The Knightian concept draws a distinction between uncertainty and risk. Optimal decisions in real options models, once discarded by the decision makers, become suboptimal choices, suggesting the presence of Knightian Uncertainty elements in the decision environment. Suboptimal decisions contradict the basic NPV rule, as the decision makers are rational by assumption. This results in a so-called “ex-post NPV” that harmonizes with that choice, according to the decision rule, by quantitatively determining a degree of uncertainty aversion. By adopting the Choquet Expected Value and a parameter representing uncertainty aversion, and by using the concept of non-additive probabilities, we obtain approximations of “post- decision NPVs” and determine the degrees of uncertainty aversion. The proposed formulation is used to evaluate an R&D project.
Keywords
Decision under uncertainty. Real Options in R&D. Economic evaluation of R&D projects. R&D incremental. Knightian Uncertainty.
References
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Dempster, A. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals Mathematical Statistics, 38, 205-247. http://dx.doi.org/10.1214/aoms/1177698950
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Ellsberg, D. (1961). Risk, Ambiguity and the Savage Axioms. Quarterly Journal of Economics, 75, 643-669. http://dx.doi.org/10.2307/1884324
Gilboa, I., & Schmeidler, D. (1989). Maxmin Expected Utility with Non-unique Prior. Journal of Mathematical Economics, 18, 141-153. http://dx.doi.org/10.1016/0304-4068(89)90018-9
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Knight, F. (1921). Risk, Boston: Hougohton PMCid:PMC1399809 . Uncertainty and Profit. Mifflin. PMid:17864564
Leite, L. A. M., Teixeira, J. P., & Samanez, C. P. (2012). Ex ante Economic Assesment in Incremental R&D Projects: Technical and Development Time Uncertainties Addressed By Real Options Theory. Pesquisa Operacional, 32(3), 617-642. http://dx.doi.org/10.1590/S0101-74382012005000025
Neumann, V., & Morgenstern, J. (1947). Theory of Games and Economic Behaviour. Princeton: Princeton University Press.
Petrobras, & Universidade Federal de Minas Gerais. (2008). Desenvolvimento de Metodologia para a Avaliação de Projetos de P & D Baseada na Teoria das Opções Reais – Relatório Final. Relatório técnico de projeto de P&D. Rio de Janeiro: Petrobras.
Samanez, C. P. (2007). Gestão de Investimentos e Geração de Valor. Pearson Prentince Hall. São Paulo.
Santiago, L. P., & Bifano, T. G. (2005). Management of R&D projects under uncertainty: A multidimensional approach to managerial flexibility. IEEE Transactions on Engineering Management, 52, 269-280. http://dx.doi.org/10.1109/TEM.2005.844465
Santiago, L. P., & Vakili, P. (2005). On the Value of Flexibility in R&D Projects. Management Science, 51, 1206-1218. http://dx.doi.org/10.1287/mnsc.1050.0387
Savage, L. J. (1954). The Foundations of Statistics (2nd ed.). New York: John Willey; Dover.
Shapley, L. S. (1972). Cores of convex Games. International Journal of Game Theory, 1, 11-26. http://dx.doi.org/10.1007/BF01753431
Schmeidler, D. (1982). Subjective Probability and Expected Utility without Additivity (pp. 84-112). CARESS, Working Paper.
Schmeidler, D. (1989). Subjective Probability and Expected Utility without Additivity. Econometrica, 57, 571-587. http://dx.doi.org/10.2307/1911053
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton: Princeton University Press. PMCid:PMC2490625.
Silva, T. A. O., & Santiago, L. P. (2009). New product development projects evaluation under time uncertainty. Pesquisa Operacional, 29, 517-532. http://dx.doi.org/10.1590/S0101-74382009000300003
Simonsen, M. H., & Werlang, S. R. C. (1991). Subadditive probabilites and portfolio Inertia. Revista de Econometria, 11(1), 1-19.
Trigeorgis, L. (1996). Real Options, Managerial Flexibility and Strategy in Resource Allocation (2nd print.). London: MIT Press.
Choquet, G. (1953). Theory of Capacities. Annales de l’institut Fourier, 5, 131-295. http://dx.doi.org/10.5802/aif.53
Coimbra-Lisboa, P. C. (2008). Uma Introdução à Escolha Individual Sob Incerteza Knightiana, notas de aula do curso sobre Teoria dos Jogos, primeira parte. Rio de Janeiro: EPGE/FGV.
Dellacherie, C. (1972). Capacités et Processus Stochastiques. Berlin: Springer-Verlag.
Dempster, A. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals Mathematical Statistics, 38, 205-247. http://dx.doi.org/10.1214/aoms/1177698950
Dixit, A. K., & Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton: Princeton University Press. PMCid:PMC1887235.
Dow, J., & Werlang, S. R. C. (1992). Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio. Econometrica, 60, 197-204. http://dx.doi.org/10.2307/2951685
Ellsberg, D. (1961). Risk, Ambiguity and the Savage Axioms. Quarterly Journal of Economics, 75, 643-669. http://dx.doi.org/10.2307/1884324
Gilboa, I., & Schmeidler, D. (1989). Maxmin Expected Utility with Non-unique Prior. Journal of Mathematical Economics, 18, 141-153. http://dx.doi.org/10.1016/0304-4068(89)90018-9
Gilboa, I. (2009). Theory of Decision Under Uncertainty. New York: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511840203
Huchzermeier, A., & Loch, C. H. (2001). Project management under risk: Using real options approach to evaluate flexibility in R&D. Management Science, 47, 85-101. http://dx.doi.org/10.1287/mnsc.47.1.85.10661
Knight, F. (1921). Risk, Boston: Hougohton PMCid:PMC1399809 . Uncertainty and Profit. Mifflin. PMid:17864564
Leite, L. A. M., Teixeira, J. P., & Samanez, C. P. (2012). Ex ante Economic Assesment in Incremental R&D Projects: Technical and Development Time Uncertainties Addressed By Real Options Theory. Pesquisa Operacional, 32(3), 617-642. http://dx.doi.org/10.1590/S0101-74382012005000025
Neumann, V., & Morgenstern, J. (1947). Theory of Games and Economic Behaviour. Princeton: Princeton University Press.
Petrobras, & Universidade Federal de Minas Gerais. (2008). Desenvolvimento de Metodologia para a Avaliação de Projetos de P & D Baseada na Teoria das Opções Reais – Relatório Final. Relatório técnico de projeto de P&D. Rio de Janeiro: Petrobras.
Samanez, C. P. (2007). Gestão de Investimentos e Geração de Valor. Pearson Prentince Hall. São Paulo.
Santiago, L. P., & Bifano, T. G. (2005). Management of R&D projects under uncertainty: A multidimensional approach to managerial flexibility. IEEE Transactions on Engineering Management, 52, 269-280. http://dx.doi.org/10.1109/TEM.2005.844465
Santiago, L. P., & Vakili, P. (2005). On the Value of Flexibility in R&D Projects. Management Science, 51, 1206-1218. http://dx.doi.org/10.1287/mnsc.1050.0387
Savage, L. J. (1954). The Foundations of Statistics (2nd ed.). New York: John Willey; Dover.
Shapley, L. S. (1972). Cores of convex Games. International Journal of Game Theory, 1, 11-26. http://dx.doi.org/10.1007/BF01753431
Schmeidler, D. (1982). Subjective Probability and Expected Utility without Additivity (pp. 84-112). CARESS, Working Paper.
Schmeidler, D. (1989). Subjective Probability and Expected Utility without Additivity. Econometrica, 57, 571-587. http://dx.doi.org/10.2307/1911053
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton: Princeton University Press. PMCid:PMC2490625.
Silva, T. A. O., & Santiago, L. P. (2009). New product development projects evaluation under time uncertainty. Pesquisa Operacional, 29, 517-532. http://dx.doi.org/10.1590/S0101-74382009000300003
Simonsen, M. H., & Werlang, S. R. C. (1991). Subadditive probabilites and portfolio Inertia. Revista de Econometria, 11(1), 1-19.
Trigeorgis, L. (1996). Real Options, Managerial Flexibility and Strategy in Resource Allocation (2nd print.). London: MIT Press.
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