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Uncertainty Economics

  • Charles S. Tapiero
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 188)

Abstract

This chapter seeks to reconcile fundamental financial approaches with uncertainty. Uncertainty is defined by the unknown rather than the predictable, counted and accounted for. While financial decisions are reached based on what we know, what we can predict and what we can presume based on experience and the rationalities that financial agents assume. The uncertainty we consider is defined in a limited sense, namely, a partial knowledge of future state preferences and their quantification. There are many approaches to do so such as negligence of the unknown, human intentional rationalities as well behavioral and psychological approaches to confront the unknown. This chapter focuses its attention on the use of entropy for “non-extensive systems” (a term commonly used in physics with its parallel in finance, which we define as “incompleteness”) based on a parametric generalization of the Boltzmann–Gibbs entropy (which assumes extensive systems). Optimization of the Tsallis parametric entropy for non-extensive systems is then used to derive implied power laws and standardized probability distributions that are both asymmetric and have fat tails. This approach provides a parametric definition of the “missing”, namely the tail probabilities not accounted for in selecting an asset future price distribution.

Subsequently, the chapter outlines a number of approaches to robust decision models and ex-post risk management. It concludes with a discussion of risk externalities in financial and environmental regulation and draws a parallel between “banks’ risks” for which they do not assume responsibility for and pollution risks of firms and consumers who consume and who do not assume their pollution consequences. Both cases, call for an efficient regulation and statistical controls which is the topic of  Chap. 11.

Keywords

Risk Model Generalize Entropy Prospect Theory Positive Externality Insurance Contract 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abdellaoui, M., & Munier, B. (1997). Experimental determination of preferences under risk: The case of very low probability radiation. Ciencia and Tecnologia dos Materiais, 9, 25–31.Google Scholar
  2. Abdellaoui, M., & Munier, B. (1999). How consistent are probability tradeoffs in individual preferences under risk? In M. J. Machina & B. Munier (Eds.), Beliefs, interactions and preferences in decision making (pp. 285–295). Dordrecht/Boston: Kluwer Academic Publishers.Google Scholar
  3. Abe, S. (1997). Physics Letters A, 224, 326.CrossRefGoogle Scholar
  4. Ahlbrecht, M., & Weber, M. (1997). Preference for gradual resolution of uncertainty. Theory and Decision, 43, 167–185.CrossRefGoogle Scholar
  5. Akturk, E., Bagci, G. B., & Sever, R. (2007). Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi entropies? asXiv:cond-mat/07032771v1, gbb0002@unt.edu.Google Scholar
  6. Allais, M. (1953). Le comportement de l'homme rationnel devant le risque, Critique des postulats et axiomes de l'ecole Americaine. Econometrica, 21, 503–546.CrossRefGoogle Scholar
  7. Amato, J. D., & Remolona, E. M. (2005). The pricing of unexpected credit losses. BIS, Working Paper No. 190.Google Scholar
  8. Ang, B. W. (1999). Is the energy intensity a less useful indicator than the carbon factor in the study of climate change? Energy Policy, 27, 943–946.CrossRefGoogle Scholar
  9. Ang, B. W., & Pandiyan, G. (1997). Decomposition of energy-induced CO2 emissions in manufacturing. Energy Economics, 19, 363–374.CrossRefGoogle Scholar
  10. Arrow, K. J. (1982). Risk perception in psychology and in economics. Economics Inquiry, 20, 1–9.CrossRefGoogle Scholar
  11. Arrow, K. J., Colombatto, E., Perlman, M., & Schmidt, C. (Eds.). (1996). The rational foundations of economic behavior. London: Macmillan.Google Scholar
  12. Aschauer, D. A. (1989a). Is public expenditure productive. Journal of Monetary Economics, 23, 177–200.CrossRefGoogle Scholar
  13. Aschauer, D. A. (1989b). Does public capital crowd out private capital. Journal of Monetary Economics, 24, 171–188.CrossRefGoogle Scholar
  14. Batten, D. F., & Karlsson, C. (Eds.). (1996). Infrastructure and the complexity of economic development (Advances in spatial science, pp. 49–60). Heidelberg and New York: Springer.CrossRefGoogle Scholar
  15. Berndt, E. R., & Harrison, B. (1991). Measuring the contribution of public infrastructure in Sweden, NBER WP n° 3842.Google Scholar
  16. Borges, E. P., & Roditi, I. (1998). A family of nonextensive entropies. Physics Letters A, 246, 399–402.CrossRefGoogle Scholar
  17. Borland, L., & Bouchaud, J. P. (2004). A non Gaussian option pricing model with skew. Quantitative Finance, 4(5), 499–514.CrossRefGoogle Scholar
  18. Brannlund, R., Ghalwash, T., & Nordstrom, J. (2006). Increased energy efficiency and the rebound effect: Effects on consumption and emissions, Energy Economics.Google Scholar
  19. Brock, W. (1986). Distinguishing random and deterministic systems. Journal of Economic Theory, 40(1), 168–195.CrossRefGoogle Scholar
  20. Brock, W. A., & Dechert, W. D. (1988). Theorems on distinguishing deterministic systems. In W. Barnett, E. Berndt, & H. White (Eds.), Dynamic econometric modeling (pp. 247–265). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  21. Brody, D. C., Buckley, I. R. C., & Constantinou, I. C. (2007). Option price calibration from Renyi entropy. Physics Letters A, 366, 298–3007.CrossRefGoogle Scholar
  22. Coase, R. H. (1937). The nature of the firm. Economica, 4(16), 386–405.CrossRefGoogle Scholar
  23. Coase, R. H. (1960). The problem of social cost. Journal of Law and Economics, 3(2), 1–44.CrossRefGoogle Scholar
  24. Debreu, G. (1953). Une economie de l’incertain. Working Paper, Electricite de France, Paris, France (Published in 1960 in Economie Appliquee 13, no.1, pp. 111–116).Google Scholar
  25. DeCanio, S. J. (1997). Economic modeling and the false tradeoff between environmental protection and economic growth. Contemporary Economic Policy, 15, 10–27.CrossRefGoogle Scholar
  26. Dembo, R. S. (1989). Scenario optimization. Algorithmics Inc. Research Paper 89.01.Google Scholar
  27. Dembo, R. S. (1993). Scenario immunization. In S. A. Zenios (Ed.), Financial optimization. London: Cambridge University Press.Google Scholar
  28. Dempster, M. A. H., Medova, E. A., & Yang, S. W. (2007). Empirical copulas for CDO tranche pricing using relative entropy, Center for Financial Research, Judge Business School, University of Cambridge, UKGoogle Scholar
  29. Dyer, J. S., & Jia, J. (1997). Relative risk-value model. European Journal of Operational Research, 103, 170–185.CrossRefGoogle Scholar
  30. Economides, N. (1996). The Economics of Networks, International Journal of Industrial Organization, vol. 14, No 2.Google Scholar
  31. Eeckhoudt, L., Gollier, C., & Schlesinger, H. (1996). Changes in background risk and risk taking behavior. Econometrica, 64, 683–689.CrossRefGoogle Scholar
  32. Eeckoudt, L., & Kimball, M. (1991). Background risk prudence and the demand for insurance. In G. Dionne (Ed.), Contributions to insurance economics. Boston: Kluwer Academic.Google Scholar
  33. Ellsberg, D. (1961). Risk, ambiguity and the savage axioms (pp. 643–669). 75: Quarterly Journal of Economics.Google Scholar
  34. Fraundorf, P. (2007). Thermal roots of correlation-based complexity. Complexity, 13(3), 18–26.CrossRefGoogle Scholar
  35. Friedman, M. (1976). Price Theory, Aldine de Gruyler.Google Scholar
  36. Friedman, M., & Savage, L. J. (1948). The utility analysis of choices involving risk. Journal of Political Economy, 56, 279–304.CrossRefGoogle Scholar
  37. Friedman, M., & Savage, L. J. (1952). The expected utility hypothesis and the measurability of utility. Journal of Political Economy, 60, 463–474.CrossRefGoogle Scholar
  38. Gibbs, J. W. (1961). The scientific papers of J.W. Gibbs (Vol. 1). New York: Dover Publications.Google Scholar
  39. Gilboa, I., & Schmeidler, D. (1995). Case-based decision theory. Quarterly Journal of Economics, 99, Août 1995. p. 605-639.Google Scholar
  40. Gollier, C., & Pratt, J. W. (1996). Risk vulnerability and the tempering effect of background risk. Econometrica, 64, 1109–1123.CrossRefGoogle Scholar
  41. Good, I. J. (1965). The estimation of probabilities: An essay on modern Bayesian methods (Research Monograph no 30). Cambridge, MA: MIT Press.Google Scholar
  42. Good, I. J. (1968). Utility of a distribution. Nature, 219, 139.CrossRefGoogle Scholar
  43. Gramlich, E. M. (1994). Infrastructure: A review essay. Journal of Economic Literature, 32, 1176–1196 (see important list of references at the end of the paper).Google Scholar
  44. Granovskii, A., Dincer, I., & Rosen, M. A. (2006). Environmental and economic aspects of hydrogen production and utilization in fuel cell vehicles. Journal of Power Sources, 157(1), 411–421.CrossRefGoogle Scholar
  45. Greaker, M. (2006). Spillovers in the development of new pollution abatement technology: A new look at the Porter-hypothesis. Journal of Environmental Economics and Management, 52, 411–420.CrossRefGoogle Scholar
  46. Greening, L. A., Greene, D. L., & Difiglio, C. (2000). Energy efficiency and consumption—The rebound effect—A survey. Energy Policy, 28, 389–401.CrossRefGoogle Scholar
  47. Jackson, F. H. (1909). Mess. Math. 38, 1909, 57, Quarterly Journal of Pure and Applied Mathematics, 41, 193.Google Scholar
  48. Jia, J., & Dyer, J. S. (1996). A standard measure of risk and risk-value models. Management Science, 42(12), 1691–1705.CrossRefGoogle Scholar
  49. Jia, J., Dyer, J. S., & Butler, J. C. (2001). Generalized disappointment models. Journal of Risk and Uncertainty, 22(1), 59–78.CrossRefGoogle Scholar
  50. Kahneman, D., Tversky, A. (1979). Prospect theory: An analysis of decision under risk, Econometrica, March, pp. 263–291.Google Scholar
  51. Kapur, J. N., & Kesavan, H. K. (1992). Entropy optimization principles with applications. San Diego, CA: Academic.Google Scholar
  52. Katz, M., & Shapiro, C. (1985). Network externalities, competition, and compatibility. American Economic Review, 75(3), 424–440.Google Scholar
  53. Kindleberger, C. (1978). Manias, panics, and crashes: a history of financial crises, Basic BooksGoogle Scholar
  54. Knight, F. (1921). Risk, uncertainty and profits. Boston, MA: Houghton, Mifflin & Co.Google Scholar
  55. Kullback, S. (1959). Information theory and statistics. New York: Wiley.Google Scholar
  56. Kullback, S. (1987). The Kullback-Leibler distance. The American Statistician, 41, 340–341.Google Scholar
  57. Kullback, S., & Leibler, R. A. (1951). On Information and sufficiency. Annals of Mathematical Statistics, 22(1), 79–86. doi: 10.1214/aoms/1177729694 DOI:10.1214%2Faoms%2F1177729694.MR39968.CrossRefGoogle Scholar
  58. Laffont, J. J. (1989). The economics of uncertainty and information. Cambridge, MA: MIT Press.Google Scholar
  59. Laffont, J. J. (1995). Regulation, moral hazard and insurance of environmental risks. Journal of Public Economics, 58, 319–336.CrossRefGoogle Scholar
  60. Langlois, N., & Cosgel, M. M. (1993). Frank Knight on risk, uncertainty and the firm: A new reinterpretations. Economic Inquiry, 31(3), 456–465.CrossRefGoogle Scholar
  61. Leland, H., & Pyle, D. (1977). Information asymmetries, financial structure and financial intermediation. Journal of Finance, 32, 371–387.CrossRefGoogle Scholar
  62. Leroy, S. F., & Singell, L. D., Jr. (1987). Knight on risk and uncertainty. Journal of Political Economy, 95(21), 394–406.CrossRefGoogle Scholar
  63. Liebowitz, S., & Margolis, S. (1994). Network externality: An uncommon tragedy. Journal of Economic Perspectives, 8(2), 133–150.CrossRefGoogle Scholar
  64. Loomes, G., & Sugden, R. (1982). Regret theory: An alternative to rational choice under uncertainty. The Economic Journal, 92, 805–824.CrossRefGoogle Scholar
  65. Loomes, G., & Sugden, R. (1987). Some implications of a more general form of regret theory. Journal of Economic Theory, 41, 270–287.CrossRefGoogle Scholar
  66. Lorenz, E. (1966). Large-scale motions of the atmosphere: Circulation. In P. M. Hurley (Ed.), Advances in earth science. Cambridge, MA: MIT Press.Google Scholar
  67. Machina, M. J. (1982). Expected utility analysis without the independence axiom. Econometrica, 50, 277–323.CrossRefGoogle Scholar
  68. Machina, M. J., & Munier, B. (Eds.). (1999). Beliefs, interactions and preferences in decision making. Boston: Kluwer Academic.Google Scholar
  69. Magill, M., & Quinzii, M. (1996). Theory of incomplete markets. Cambridge, MA: MIT Press.Google Scholar
  70. Mandelbrot, B. (1997). Three fractal models in finance: Discontinuity, concentration, risk. Economic Notes, 26, 171–212.Google Scholar
  71. Mandelbrot, B., & Wallis, J. (1968). Noah, Joseph and operational hydrology. Water Resources Research, 4, 909–918.CrossRefGoogle Scholar
  72. May, R. (1974). Biological populations with non-overlapping generations: Stable points, stable cycles, and chaos. Science, 186, 645–647.CrossRefGoogle Scholar
  73. Morrison, C., & Schwartz, A. (1996). State infrastructure and productive performance. American Economic Review, 86, 1095–1111.Google Scholar
  74. Mulvey, J. M., Vanderbei, R.J., & Zenios, S.A. (1991). Robust optimization of large scale systems. Report SOR 13, Princeton University.Google Scholar
  75. Munier, B. (1986). Complexité et Décision stratégique dans l'Incertain : Que peut-on retenir de la Théorie?. In: Boiteux, M., Th. de Montbrial and B. Munier, eds., Marchés, Capital et Incertitude, Paris, Economica.Google Scholar
  76. Munier, B. (1991). Market uncertainty and the process of belief formation. Journal of Risk and Uncertainty, 4, 233–250.CrossRefGoogle Scholar
  77. Munier, B. (1995). From instrumental to cognitive rationality: Contributions of the last decade to risk modeling. Revue d'Economie Politique, 105, 5–70 (French, with abstract in English).Google Scholar
  78. Munier, B. (Ed.). (2012). Global uncertainty and the volatility of agricultural commodities. Amsterdam, The Netherlands: IOS Press.Google Scholar
  79. Munier, B., Selten, R., et al. (1999). Bounded rationality modeling. Marketing Letters, 10(3), 233–248.CrossRefGoogle Scholar
  80. Munnell, A. H. (1992). Infrastructure investment and economic growth. Journal of Economic Perspectives, 6, 189–198.CrossRefGoogle Scholar
  81. Nau, R. (2011). Risk, ambiguity and state-preference theory. Economic Theory, 48(2–3), 437–467.CrossRefGoogle Scholar
  82. Naudts, J. (2007). Generalized thermostatistics. Belgium: University of Antwerpen.Google Scholar
  83. Nijkamp, P., & Blaas, E. (1993). Impact assessment and evaluation in transportation planning. Amsterdam: Kluwer Academic.Google Scholar
  84. Peter, E. E. (1995). Chaos and order in capital markets. New York: Wiley.Google Scholar
  85. Rabin, M. (1998). Psychology and economics. Journal of Economic Literature, 36, 11–46.Google Scholar
  86. Riordan, M. (1984). Uncertainty, asymmetric information and bilateral contracts. Review of Economic Studies, 51, 83–93.CrossRefGoogle Scholar
  87. Rockafellar, R. T., & Wets, R. J.-B. (1992). A dual strategy for the implementation of the aggregation principle in decision making under uncertainty. Applied Stochastic Models and Data Analysis, 8, 245–255.CrossRefGoogle Scholar
  88. Rubinstein, A. (1998). Modeling bounded rationality. Cambridge, MA: MIT Press.Google Scholar
  89. Samuelson, P. A. (1963). Risk and uncertainty: A fallacy of large numbers. Scientia, 98, 108–163.Google Scholar
  90. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6, 41–49.Google Scholar
  91. Sanchez-Robles, B. (1998a). The Role of Infrastructure Investment in Development: Some Macroeconomic Considerations International-Journal-of-Transport-Economics; 25(2), June, pages 113-36. http://wwwdte.spol.uniroma1.it/trasporti/journal.html
  92. Sanchez-Robles, B. (1998b). Infrastructure investment and growth: Some empirical evidence. Contemporary Economic Policy, 16(1), 98–108.CrossRefGoogle Scholar
  93. Sato, A.-H. (2010). q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series, Mathematical Analysis of Generalized Entropies and their Applications,, Journal of Physics, Conference Series 201, 012008Google Scholar
  94. Simon, H. A. (1979). Models of man. New Haven, CT: Yale University Press.Google Scholar
  95. Simon, H. A. (1982). Models of bounded rationality (Vol. 2). Cambridge, MA: MIT Press.Google Scholar
  96. Stanley, M. H. R., Amaral, L. A. N., Bulkdyrev, S. V., Havlin, S. V., Leschron, H., Mass, P., Salinger, M. A., & Stanley, H. E. (1996). Nature, 397, 804.CrossRefGoogle Scholar
  97. Taleb, N. N. (2007). The Black Swan: The impact of the highly improbable. New York: Random House.Google Scholar
  98. Taleb, N. N. (2008). The fourth quadrant: A map of the limits of statistics. Edge, http://www.edge.org/3rd_culture/taleb08/taleb08_index.html.
  99. Taleb, N. N. (2009). Errors, robustness, and the fourth quadrant. International Journal of Forecasting, 25(4), 744–759.CrossRefGoogle Scholar
  100. Taleb, N. N., & Tapiero, C.S. (2010). Risk Externalities and Too Big to Fail, Physica A: Statistical Mechanics and Applications 2010Google Scholar
  101. Tapiero, C. (1995a). Complexity and industrial systems. Special Issue Editor, RAIRO. Google Scholar
  102. Tapiero, C. S. (1995b). Acceptance sampling in a producer-supplier conflicting environment: Risk neutral case. Applied Stochastic Models and Data Analysis, 11, 3–12.CrossRefGoogle Scholar
  103. Tapiero, C. S. (2005a). Risk management, encyclopedia on actuarial and risk management. New York and London: Wiley.Google Scholar
  104. Tapiero, O. (2012). Implied Risk neutral Distribution: The Non Extensive Entropy Approach, Ph.D Dissertation, Bar Ilan University, Israel.Google Scholar
  105. Thaler, R. H., et al. (1997). The effect of myopia and loss aversion on risk taking: An experimental test. Quarterly Journal of Economics, 112, 647–661.CrossRefGoogle Scholar
  106. Tversky, A., & Kahneman, D. (1992). Advances is prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323.CrossRefGoogle Scholar
  107. Wakker, P. P. (1994). Separating marginal utility and probabilistic risk aversion. Theory and Decision, 36, 1–44.CrossRefGoogle Scholar
  108. Wakker, P. P. (2001). On the composition of risk preference and belief. Psychological Review, 111, 236–241.CrossRefGoogle Scholar
  109. Wakker, P. P. (2010). Prospect theory for risk and ambiguity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  110. Wakker, P., & Tversky, A. (1993). An axiomatization of cumulative prospect theory. Journal of Risk and Uncertainty, 7, 147–176.CrossRefGoogle Scholar
  111. Weston, J. F. The profit concept and theory: A restatement. Journal of Political Economy, 62((2), 152–170.Google Scholar
  112. Xepapadeas, A. P. (1994). Controlling environmental externalities: Observability and optimal policy rules. In C. Dosi & T. Tomasi (Eds.), Nonpoint source pollution regulation: Issues and analysis. Dordrecht: Kluwer Academic.Google Scholar
  113. Xepapadeas, A. P. (1995). Observability and choice of instrument mix in the control of externalities. Journal of Public Economics, 56, 485–498.CrossRefGoogle Scholar
  114. Renyi, A. (1961). On measures of entropy and information. In Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability; Statistical Laboratory of the University of California, Berkeley, CA, USA, 20 June–30 June, 1960; University of California Press: Berkeley, California, 1961; Volume 1, pp. 547–561.Google Scholar
  115. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 479–488.CrossRefGoogle Scholar

Copyright information

© Charles S. Tapiero 2013

Authors and Affiliations

  • Charles S. Tapiero
    • 1
  1. 1.Department of Finance and Risk EngineeringPolytechnic Institute of New York UniversityBrooklynUSA

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