Non-Expected Utility and Risk Management pp 135-150 | Cite as

# Functional Form Problems in Modeling Insurance and Gambling

Chapter

## Abstract

Defining the outputs of the property insurance and gambling sectors of an economy has proved to be a difficult problem for national income accountants. It is well known that the traditional expected-utility model is not consistent with economic agents fully insuring their property. Thus the present paper adapts existing non-expectedutility theories to yield useful measures of output for the property insurance and gambling sectors.

## Key words

non-expected utility gambling insurance functional form problems risky activities in the national accounts state contingent commodities## Preview

Unable to display preview. Download preview PDF.

## References

- ALLAIS, M. [ 1953 ]: “Le comportement de l’homme rationnel devant le risque: critique de postulats et axiomes de l’école américains,”
*Econometrica*, 21, 503–546.CrossRefGoogle Scholar - ARROW, K.J. [ 1951 ]: “Alternative Approaches to the Theory of Choice in Risk-Taking Situations,”
*Econometrica*, 19, 404–437.CrossRefGoogle Scholar - ARROW, K.J. [ 1953 ]: “Le role des valeurs boursières pour le répartition la meilleure des risques.” In
*Économétrie*, Centre National de la Recherche Scientifique, Paris (41–48). Reprinted in English translation in 1964 as “The Role of Securities in the Optimal Allocation of Risk-Bearing,”*Review of Economic Studies*, 31, 91–96.Google Scholar - BLACKORBY, C., DAVIDSON, R., and DONALDSON, D. [ 1977 ]: `A Homiletic Exposition of the Expected Utility Hypothesis,“
*Economica*, 44, 351–358.CrossRefGoogle Scholar - CHEW, S.H. [ 1983 ]: “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox,”
*Econometrica*, 51, 1065–1092.CrossRefGoogle Scholar - CHEW, S.H. [ 1989 ]: “Axiomatic Utility Theories with the Betweenness Property,”
*Annals of Operations Research*, 19, 273–298.CrossRefGoogle Scholar - CHEW, S.H., and EPSTEIN, L.G. [ 1989a ]: “A Unifying Approach to Axiomatic Non-Expected Utility Theories,”
*Journal of Economic Theory*, 49, 207–240.CrossRefGoogle Scholar - CHEW, S.H., and EPSTEIN, L.G. [ 1989b ]: “The Structure of Preferences and Attitudes Towards the Timing of the Resolution of Uncertainty,”
*International Economic Review*, 30, 103–117.CrossRefGoogle Scholar - CHEW, S.H., and EPSTEIN, L.G. [ 1990 ]: “Nonexpected Utility Preferences in a Temporal Framework with an Application to Consumption-Savings Behavior,”
*Journal of Economic Theory*, 50, 54–81.CrossRefGoogle Scholar - DEBREU, G. [ 1959 ]:
*Theory of Value*. Wiley, New York.Google Scholar - DEKEL, E. [ 1986 ]: “An Axiomatic Characterization of Preferences Under Uncertainty: Weakening the Independence Axiom,”
*Journal of Economic Theory*, 40, 304–318.CrossRefGoogle Scholar - DENNY, M. [ 1980 ]: “Measuring the Real Output of the Life Insurance Industry: A Comment,”
*Review of Economics and Statistics*, 62, 150–152.CrossRefGoogle Scholar - DIEWERT, W.E. [ 1993 ]: “Symmetric Means and Choice Under Uncertainty,” in
*Essays in Index Number Theory*(Vol. 1), W.E. Diewert and A.O. Nakamura (Eds.), North-Holland, Amsterdam (355–433).Google Scholar - EPSTEIN, L.G. [ 1992 ]: “Behavior Under Risk: Recent Developments in Theory and Applications,”
*in Advances in Economic Theory*, J.J. Laffont (Ed.), Cambridge University Press, New York.Google Scholar - EPSTEIN, L.G., and ZIN, S.E. [ 1989 ]: “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework,”
*Econometrica*, 57, 937–969.CrossRefGoogle Scholar - EPSTEIN, L.G., and ZIN, S.E. [ 1990 ]: “First Order Risk Aversion and the Equity Premium Puzzle,”
*Journal of Monetary Economics*, 26, 387–407.CrossRefGoogle Scholar - EPSTEIN, L.G., and ZIN, S.E. [ 1991a ]: “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis,”
*Journal of Political Economy*, 99, 263–286.CrossRefGoogle Scholar - EPSTEIN, L.G., and ZIN, S.E. [ 1991b ]: “The Independence Axiom and Asset Returns,” Technical Working Paper No. 109, National Bureau of Economic Research, Cambridge (Mass.).Google Scholar
- FARMER, R.E.A. [ 1990 ]: “Rince Preferences,”
*Quarterly Journal of Economics*, 105, 43–60.CrossRefGoogle Scholar - GORMAN, W.M. [ 1968 ]: “The Structure of Utility Functions,”
*Review of Economic Studies*, 35, 367–390.CrossRefGoogle Scholar - GUL, F. [ 1991 ]: “A Theory of Disappointment Aversion,”
*Econometrica*, 59, 667–686.CrossRefGoogle Scholar - HIRSHHORN, R., and GEEHAN, R. [ 1977 ]: “Measuring the Real Output of the Life Insurance Industry,’
*Review of Economics and Statistics*, 59, 211–219.CrossRefGoogle Scholar - Hirshleifer, J. [ 1965 ]: “Investment Decision Under Uncertainty: Choice-Theoretic Approaches,”
*Quarterly Journal of Economics*, 79, 509–536.CrossRefGoogle Scholar - HORNSTEIN, A., and PRESCOTT, E.C. [ 1991 ]: “Insurance Contracts as Commodities: A Note,”
*Review of Economics Studies*, 58, 917–928.CrossRefGoogle Scholar - KREPS, D., and PORTEUS, E. [ 1978 ]: “Temporal Resolution of Uncertainty and Dynamic Choice Theory,”
*Econometrica*, 46, 185–200.CrossRefGoogle Scholar - KREPS, E., and PORTEUS, E. [ 1979 ]: “Temporal Von Neumann-Morgenstern and Induced Preferences,”
*Journal of Economic Theory*, 20, 81–109.CrossRefGoogle Scholar - MACHINA, M. [ 1982 ]: “ `Expected Utility’ Analysis Without the Independence Axiom:’
*Econometrica*, 50, 277–323.CrossRefGoogle Scholar - MACHINA, M. [ 1995 ]: “Non-Expected Utility and the Robustness of the Classical Insurance Paradigm,”
*The Geneva Papers on Risk and Insurance Theory*, 20, 9–50.CrossRefGoogle Scholar - RUGGLES, R. [ 1983 ]: “The United States National Income Account, 1947–1977: Their Conceptual Basis and Evolution,”
*in The U.S. National Income and Product Accounts: Selected Topics*, M. Foss (Ed.), NBER Studies in Income and Wealth, Vol. 47, University of Chicago Press, Chicago (15–96).Google Scholar - SAMUELSON, P.A. [ 1952 ]: “Probability Utility and the Independence Axiom,”
*Econometrica*, 20, 670–678. SAMUELSON, P.A. [1960]: “The St. Petersburg Paradox as a Divergent Double Limit,”*International Economic Review*, 1, 31–37.CrossRefGoogle Scholar - SEGAL, W., and SPIVAK, A. [199% “First Order versus Second Order Risk Aversion:’
*Journal of Economic Theory*,*51*, 11–125.Google Scholar - WEIL, P. [ 1990 ]: “Nonexpected Utility in Macroeconomics,”
*Quarterly Journal of Economics*, 105, 29–42. YAARI, M. [1965]: “Convexity in the Theory of Choice Under Risk,”*Quarterly Journal of Economics*, 79, 278–290.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1995