Abstract
Risk aversion has formed an integral part in most applied decision models under uncertainty, where the latter is generated by a probabilistic mechanism. This mechanism is not completely known, so that the environment under which decisions are to be made is random. However, the source of randomness may differ from one application to another, hence the decision-making response may vary. For example, in micro-economic models, consumer’s or producer’s response behavior is analyzed under conditions of price or cost parameter uncertainty and this behavior is compared with the case when there is no uncertainty. In engineering systems having a number of channels, the reliability levels may vary between channels and the noise elements may vary: the decision problem is one of maximizing the system reliability. In quality control, a sample inspection plan seeks to determine an acceptable quality level (AQL) of a product lot by minimizing the cost of making wrong decisions, where the latter involves producer’s risk (α) and consumer’s risk (β). The probability that a sampling plan will reject AQL is called the producer’s risk a i.e. the Type I error, whereas the probability that the plan will accept fraction-defective levels (FDL) is called consumer’s riskβ i.e. the Type II error. Usually, if the lot quality is equal to or better than AQL quality, p a is equal to or greater than (1 — α), where p a denotes the probability of acceptance which is usually 0.95 i.e. α = 0.05. Similarly, if the lot quality is equal to or worse than FDL quality, p a is equal to or less thanβ, the Type II decision error and p a is usually 0.10.
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References
Amihud, Y: “On the Consumer Demand Theory Under Uncertainty”, in R. Henn and O. Moeschlin, eds.: Mathematical Economics and Game Theory: Essays in Honor of Oskar Morgenstern. Springer-Verlag: Berlin, 1977
Arrow, K. J.: “Value and Demand for Information”, in K. J. Arrow: Essays in the Theory of Risk Bearing. North Holland: Amsterdam, 1971
Batra, R.N.: The Pure Theory of International Trade Under Uncertainty. John Wiley: New York, 1975
Behara, M.: “Entropy and Utility”, in G. Menges, ed. Information, Inference and Decision. Reidel Publishing: Dordrecht, Holland, 1974, pp. 145–154
Binswanger, H.P.: “Risk Attitudes of Rural Households in Semi-Arid Tropical India”, Economic and Political Weekly, June 1978, 49–62
Buhlmann, H.: “Minimax Credibility”, in P.M. Kahn, ed. Credibility: Theory and Applications. Academic Press: New York, 1975, pp. 1–18
Bury, K.V.: “Design Optimization Under Cost Uncertainty and Risk Aversion”, Infor, 14 (1976), 250–258.
Charnes, A., Cooper, W.W. and D.B. Learner: “Constrained Information Theoretic Characterizations in Consumer Purchase Behavior”, Journal of Operational Research, 29 (1978), 833–842
Charnes, A., Cooper, W.W. and E. Rhodes: “Measuring the Efficiency of Decision- Making Units”, European Journal of Operational Research, 2 (1978), 429–444
Chernoff, H.: “Sequential Analysis and Optimal Design”, Society for Industrial and Applied Mathematics: Philadelphia, 1972
Chernoff, H. “Some Measures for Discriminating Between Normal Multivariate Distributions with Unequal Covariance Matrices”, in P.R. Krishnaiah, ed. Multivariate Analysis III. Academic Press: New York, 1973, 337–344
Chu, K.C.: “Designing Information Structures for Quadratic Decision Problems”, Journal of Optimization Theory and Applications, 25 (1978), 139–160
Debreu, G.: “The Coefficient of Resource Utilization”, Econometrica, 19 (1951), 273–292
Duncan, G.T.: “A Matrix Measure of Multivariate Local Risk Aversion”, Econometrica, 45 (1977), 895–904
Fama, E.F. and M.H. Miller: The Theory of Finance, Holt, Renehart and Winston: New York, 1972
Farrar, D.E.: The Investment Decision Under Uncertainty, Prentice-Hall: Englewood Cliffs, N.J., 1962
Hanoch, G.: “Risk Aversion and Consumer Preferences”, Econometrica, 45 (1977), 413–426
James, A.T.: “The Variance Information Manifold and the Functions on It”, in P.R. Krishnaiah, ed., Multivariate Analysis, Vol. 3, Academic Press: New York, 1973
Johansen, L.: “Targets and Instruments Under Uncertainty”, in H.C. Bos, H. Linne- mann and P. de Wolff, eds., Economic Structure and Development: Essays in Honor of Jan Tinbergen. North Holland: Amsterdam, 1973
Johansen, L.: “Parametric Certainty Equivalence Procedures in Decision-Making Under Uncertainty”. Memorandum of Institute of Economics, University of Oslo, September 1979
Johnson, R.M.: “Multiple Discriminant Analysis: Marketing Research Applications”, in J.N. Sheth, ed., Multivariate Methods for Market and Survey Research. American Marketing Association: Chicago, 1977
Judge, G.G. and M.E. Brock: The Statistical Implications of Pre-Test and Stein-Rule Estimators, in Econometrics. North Holland: Amsterdam, 1978
Just, R.E.: “An Investigation of the Importance of Risk in Farmers Decisions”, American Journal of Agricultural Economics, 56 (1975), 14–25
Lancaster, K.: Variety, Equity and Efficiency. Columbia University Press: New York, 1979
Levin, R.D. and M. Tribus, eds.: The Maximum Entropy Formalism. MIT Press: Cambridge, 1978
Lindley, D.V.: “On a Measure of Information Provided by an Experiment”. Annals of Mathematical Statistics, 27 (1956), 986–1005
Mardia, K.V.: “Mahalanobis Distance and Angles”, in P.R. Krishnaiah, ed., Multivariate Analysis, I V. North Holland: Amsterdam, 1977
Marschak, J.: “Elements for a Theory of Teams”, Management Science, 1 (1955), 127–137
Morishima, M.: Theory of Economic Growth. Clarendon Press: Oxford, 1969
Patil, G.P. and Others: Statistical Ecology, Vol. 1: Spatial Patterns and Statistical Distributions. Pennsylvania State University Press: Pennsylvania, PA 1971
Peleg, B. and M.E. Yaari: “A Price Characterization of Efficient Random Variables”, Econometrica, 43 (1975), 283–292
Pielou, E.C.: Ecological Diversity. John Wiley: New York, 1975
Pratt, J.: “Risk Aversion in the Small and in the Large”, Econometrica, 32 (1964), 122–136
Pyatt, G.: “A Model of Brand Loyalties”, in M.G. Kendall, ed., Mathematical Model Building in Economics and Industry. Second Series. Charles Griffin: London, 1970
Schneeweiss, H.: “On the Consistency of Classical Decision Criteria”, in Inference and Decision. Toronto University Press, Toronto, 1973
Sengupta, J.K.: Stochastic Programming: Methods and Applications. North Holland: Amsterdam, 1972
Sengupta, J.K.: “Regression and Programming: Overview of Linkages”, IIMC Working Paper No. 16, Calcutta, 1976
Sengupta, J.K.: “Adaptive Decision Rules for Stochastic Linear Programming”. International Journal of Systems Science. 9 (1978), 97–109
Sengupta, J.K.: “Multiple Criteria Decisions Under Risk”, Working Paper in Economics #132. University of California, Santa Barbara, 1979
Sengupta, J.K. and R.I. Sfeir: “Risk in Supply Response”, Economics Working Paper, University of California, Santa Barbara, 1979
Sengupta, J.K.: “Constrained Games as Complementary Eigenvalue Problems”. Journal of Mathematical Analysis and Applications, 73 (1980), 301–314
Sengupta, J.K.: Decision Models in Stochastic Programming. To be published by Elsevier-North Holland: New York, ca 1980
Sengupta, J.K.: “Constrained Nonzero-Sum Games with Partially Controllable Strategies”. Journal of Optimization Theory and Applications, 31 (1980), July
Sengupta, J.K.: “Stochastic Programming: A Selective Survey of Recent Economic Applications”, Chap. 30, Stochastic Programming, ed. by M.A.H. Dempster. Academic Press: London, 1980
Sengupta, J.K. and Subhash C. Ray: “Efficiency in Activity Analysis Models: Econometric Measurements and Tests”. Department of Economics, University of California, Santa Barbara, 1980
Sengupta, J.K. and R.E. Sfeir: “Allocative Behavior Under Risk Aversion Through Quadratic Programming Experiments”. To be published in Applied Economics, ca 1981
Spence, M.: “Product Selection, Fixed Costs and Monopolistic Competition”. Review of Economic Studies, 43 (1976) 217–236
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© 1985 Martinus Nijhoff Publishers, Dordrecht
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Sengupta, J.K. (1985). Risk aversion in decision models. In: Information and Efficiency in Economic Decision. Advanced Studies in Theoretical and Applied Econometrics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5053-5_15
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DOI: https://doi.org/10.1007/978-94-009-5053-5_15
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