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The Use of Utility Functions for Investment Channel Choice in Defined Contribution Retirement Funds. I: Defence

Published online by Cambridge University Press:  10 June 2011

R.J. Thomson
R.J. Thomson
Affiliation:
School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg, Private Bag 3, WITS 2050, South Africa., Tel: +27-(0)11-646-5332, Fax: +27-(0)11-339-6640, Email: [email protected]
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Abstract

This paper addresses the use of expected utility theory for the recommendation of an apportionment between investment channels of a member's interest in a defined contribution retirement fund. Such usage is defended against arguments that have been levelled against expected utility theory and empirical evidence is discussed.

Keywords

Decision TheoryExpected Utility TheoryOptimisationInvestment Channel ChoiceDefined-Contribution Retirement FundsDynamic Programming
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 9 , Issue 3 , 01 August 2003 , pp. 653 - 709
Copyright
Copyright © Institute and Faculty of Actuaries 2003

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References

Akerlof, G. (1970). The market for ‘lemons’: qualitative uncertainty and the market echanism. Quarterly Journal of Economics, 84, 488–500.CrossRefGoogle Scholar
Alchian, A. (1953). The meaning of utility measurement. American Economic Review, 43, 26–50.Google Scholar
Allais, M. (1953). Le comportement de l'homme rational devant le risque: critique des postulats et axioms de l'école Américaine. Econometrica, 21, 503–546.CrossRefGoogle Scholar
Allais, M. (1987). The general theory of random choices in relation to the invariant cardinal tility function and the specific probability function: the (U, θ|model — a general overview. Centre National de la Recherche Scientifique.Google Scholar
Allais, M. & Hagen, O. (Eds.) (1979). Expected utility hypothesis and the Allais paradox. Reidel, Dordrecht.CrossRefGoogle Scholar
Anand, P. (1993). Foundations of rational choice with risk. Clarendon, Oxford.Google Scholar
Arrow, K.J. (1951). Social choice and individual values. 2nd ed. 1963. Wiley.Google Scholar
Arrow, K.J. (1982). Risk perception in psychology and economics. Economic Inquiry, 20, 1–9.CrossRefGoogle Scholar
Ash, R.B. (1972). Real analysis and probability. Academic, New York.Google Scholar
Aumann, R.J. (1962). Utility theory without the completeness axiom. Econometrica, 30, 445–462.CrossRefGoogle Scholar
Becker, G.M., DeGroot, M.H. & Marschak, J. (1963). An experimental study of some stochastic models for wagers. Behavioral Science, 8, 199–202.CrossRefGoogle Scholar
Bem, D.J. (1972). Self-perception. In Berkowitz (1972).Google Scholar
Bentham, J. (1776). A fragment on government. In Coker (1938).Google Scholar
Berkeley, D. & Humphreys, P. (1982). Structuring decision problems and the ‘bias’ heuristic. Acta Psychologica, 50, 201–252.CrossRefGoogle Scholar
Berkowitz, L. (1972). Advances in experimental psychology. Academic, New York.Google Scholar
Bernoulli, D. (1738). Specimen theoriae novae de mensura sortis. English translation in Econometrica, 22 (1954), 23–36.CrossRefGoogle Scholar
Bernoulli, N. (1975). Correspondence with G. Cramer (1728). In Van der Waerden (1975) Vol. 3, 555–567. Cited in Shafer (1988).Google Scholar
Booth, P. (1997). The analysis of actuarial investment risk, Actuarial research paper no. 93. Department of Actuarial Science & Statistics, City University, London.Google Scholar
Booth, P., Chadburn, R. & Ong, A. (1993). A utility maximisation approach to asset allocation. Actuarial research report no. 55. Department of Actuarial Science & Statistics, City University, London.Google Scholar
Borch, K. & Mossin, J. (Eds.) (1968). Risk and uncertainty. Macmillan, New York.Google Scholar
Bowers, L.N., Gerber, H.U., Hickman, J.C., Jones, A.J. & Nesbitt, C.J. (1986). Actuarial mathematics. Society of Actuaries.Google Scholar
Chipman, J.S.et al. (Eds.) (1971). Preferences, utility and demand: a Minnesota symposium. Harcourt, New York.Google Scholar
Clarkson, R.S. (1990). The assessment of financial risk. Transactions of the 1st AFIR International Colloquium, 2, 171–194.Google Scholar
Clarkson, R.S. (1996). Financial economics — an investment actuary's viewpoint. British Actuarial Journal, 2, 809–973.CrossRefGoogle Scholar
Coker, F.W. (Ed.) (1938). Readings in political philosophy, 2nd ed.MacMillan, New York.Google Scholar
Croce, B. (1901). Correspondence with V. Pareto in On the economic principle: a correspondence between B., Croce and V., Pareto. International Economic Papers, London, 1953, no. 3; cited in Kauder (1965: 117).Google Scholar
Deboni, L., Montesano, A. & Lines, M. (Eds.) (1986). Recent developments in the foundations of utility and risk theory. D., Reidel, Dordrecht.CrossRefGoogle Scholar
Dyer, J.S. & Sarin, R.K. (1982). Relative risk aversion. Management Science, 28, 875–886.CrossRefGoogle Scholar
Edwards, W. (Ed.) (1992). Utility theories: measurements and applications: studies in risk and uncertainty. Kluwer, Boston.CrossRefGoogle Scholar
Eichberger, J. & Harper, I.R. (1997). Financial economics. Oxford University Press, Oxford.CrossRefGoogle Scholar
Ellsburg, D. (1961). Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics, 75, 643–669.CrossRefGoogle Scholar
Faculty & Institute of Actuaries (2000). Core reading, Subject 109. Faculty & Institute of Actuaries, Oxford.Google Scholar
Festinger, L. (1957). A theory of cognitive dissonance. Stanford.CrossRefGoogle Scholar
Fishburn, P.C. (1981). Subjective expected utility. Theory and Decision, 13, 139–199.CrossRefGoogle Scholar
Fishburn, P.C. (1982). The foundations of expected utility theory. Reidel, Dordrecht.CrossRefGoogle Scholar
French, S. (1986). Decision theory: an introduction to the mathematics of rationality. Wiley, New York.Google Scholar
Friedman, M. & Savage, L.J. (1948). The utility analysis of choices involving risk. Journal of Political Economy, 56, 279–304.CrossRefGoogle Scholar
Fry, T.C. (1928). Probability and its engineering uses. Van Nostrand, Toronto.Google Scholar
Green, H.A. (1971). Consumer theory. Penguin, Hammondsworth.Google Scholar
Harsanyi, J.C. (1955). Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy, 63, 309–321.CrossRefGoogle Scholar
Hershey, J.C., Kunreuther, H.C. & Schoemaker, P.J.H. (1982). Sources of bias in assessment procedures for utility functions. Management Science, 28, 936–954.CrossRefGoogle Scholar
Howard, R.A. (1992). In praise of the old time religion. In Edwards (1992), 27–55.CrossRefGoogle Scholar
Hume, D. (1739). A treatise of human nature. London.Google Scholar
Kahnemann, D. & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
Katz, D. (1960). The functional approach to the study of attitudes. Public Opinion Quarterly, 24, 163–204.CrossRefGoogle Scholar
Kauder, E. (1965). A history of marginal utility theory. Princeton University Press, Princeton.CrossRefGoogle Scholar
Kaysen, C. (1947). A revolution in economic theory? Review of Economic Studies, 14, 1–15.CrossRefGoogle Scholar
Keeney, R.L. (1976). A group preference axiomatisation with cardinal utility. Management Science, 23, 140–145.CrossRefGoogle Scholar
Keeney, R.L. (1992). On the foundations of prescriptive decision analysis. In Edwards (1992).CrossRefGoogle Scholar
Keller, L.R. (1985). The effects of problem representation on the sure thing and substitution principles. Management Science, 31, 738–751.CrossRefGoogle Scholar
Kotz, S., Johnson, N.L. & Read, C.B. (Eds.) (1988). Encyclopaedia of statistical sciences. Wiley, New York.Google Scholar
Krzysztofowicz, R. (1983). Strength of preference and risk attitude in utility measurement. Organizational Behavior and Human Performance, 31, 88–113.CrossRefGoogle Scholar
Kyburg, H.E. & Smokler, H.E. (Eds.) (1964). Studies in subjective probability. Wiley, New York.Google Scholar
Lee, W. (1971). Decision theory and human behaviour. Wiley, New York.Google Scholar
Lichtenstein, S. & Slovic, P. (1971). Reversals of preference between bids and choices in gambling decisions. Journal of Experimental Psychology, 89, 46–55.CrossRefGoogle Scholar
Lichtenstein, S. & Slovic, P. (1973). Response-induced reversals of preferences in gambling: an extended replication in Las Vegas. Journal of Experimental Psychology, 101, 16–20.CrossRefGoogle Scholar
Luce, R.D. & Raiffa, H. (1957). Games and decisions: introduction and critical survey. Wiley.Google Scholar
Lyons, D. (1965). Forms and limits of utilitarianism. Clarendon, Oxford.CrossRefGoogle Scholar
MacCrimmon, K.R. (1965). An experimental study of the decision making behavior of business executives. Unpublished dissertation, University of California, Los Angeles.Google Scholar
MacCrimmon, K.R. (1968). Descriptive and normative implications of decisions theory postulates. In Borch, & Mossin, (1968), 3–23.Google Scholar
MacCrimmon, K.R. & Larsson, S. (1979). Utility theory: axioms versus ‘paradoxes’. In Allais, & Hagen, (1979).Google Scholar
Machina, M.J. (1982). A stronger characterisation of declining risk aversion. Econometrica, 50, 1069–1079.CrossRefGoogle Scholar
Markowitz, H.M. (1959). Portfolio selection, 2nd ed. (1991). Blackwell, Oxford.Google Scholar
Marshall, A. (1920). Principles of economics, 8th ed. MacMillan, London.Google Scholar
Menger, K. (1934). Das unsicherheitsmoment in der wertlehre. Betrachtungen in anschluss an das sogenannte Petersburger Spiel. Zeitschrift för Nationaloekonomie, 5, 459–485. In German. Also in English (Menger, 1967). Cited in Shafer (1988).CrossRefGoogle Scholar
Menger, K. (1967). The role of uncertainty in economics. Chap. 16 in Shubik (1967). Translated from Menger (1934).Google Scholar
Mill, J.S. (1863). Utilitarianism. In Mill (1910).Google Scholar
Mill, J.S. (1910). Utilitarianism; liberty; representative government. Dent, London.Google Scholar
Miller, M.H. & Modigliani, F. (1961). Dividend policy, growth and the valuation of shares. Journal of Business, 34, 411–433.CrossRefGoogle Scholar
Moskowitz, H. (1974). Effects of problem representation and feedback on rational behavior in Allais and Morlat-type problems. Decision Sciences, 5, 225–241.CrossRefGoogle Scholar
Moskowitz, H. (1975). Consistent choices and the Allais problem; empirical results on the effects of presentation and feedback. In White, & Brown, (1975), 328–340.Google Scholar
Popper, K.R. (1962). The open society and its enemies; Vol II: The high tide of prophecy: Hegel, Marx and the aftermath. Routledge & Keegan Paul, London, 4th ed.Google Scholar
Quiggin, J. (1993). Generalized expected utility theory. Kluwer, Boston.CrossRefGoogle Scholar
Raiffa, H. (1961). Risk, ambiguity and the Savage axioms: comment. Quarterly Journal of Economics, 75, 690–694.CrossRefGoogle Scholar
Ramsay, C.M. (1993). Loading gross premiums for risk without using utility theory. Transactions of the Society of Actuaries, 45, 305–349.Google Scholar
Ramsay, F.P. (1931). Truth and probability. In The logical foundations of mathematics and other essays. Kegan Paul. Reprinted in Kyburg & Smokler (1964), 61–92.Google Scholar
Richter, M.K. (1971). Rational choice. In Chipman (1971).Google Scholar
Riley, J. (1988). Liberal utilitarianism. Cambridge.Google Scholar
Ross, S.A. (1981). Some stronger measures of risk aversion in the small and the large with applications. Econometrica, 49, 621–638.CrossRefGoogle Scholar
Samuelson, P.A. (1952). Utility, preference and probability: a paper given before the conference on Les Fondements et Applications de la Theéorie du Risque en Econométrie, May 1952. Reprinted as Chap. 13 in Samuelson (1966).Google Scholar
Samuelson, P.A. (1966). The collected scientific papers of Paul A. Samuelson, Vol. 1. J.E., Stiglitz (ed.). M.I.T. Press, Cambridge, Mass.Google Scholar
Savage, L.J. (1954). The foundations of statistics. Wiley. 2nd ed.Dover, New York (1972).Google Scholar
Schoemaker, P.J.H. (1980). Experiments on decisions under risk: the expected utility hypothesis. Nijhoff, Boston.CrossRefGoogle Scholar
Sen, A. (1986). Rationality and uncertainty. In Deboni, Montesano & Lines (1986).CrossRefGoogle Scholar
Shafer, G. (1988). The St. Petersburg paradox. In Kotz, Johnson & Read (1988), Vol. 8.Google Scholar
Shubik, M. (Ed.) (1967). Essays in mathematical economics in honor of Oskar Morgenstern. Princeton University Press, Princeton.CrossRefGoogle Scholar
Slovic, P., Fischhoff, B. & Lichtenstein, S. (1977). Behavioural decision theory. Annual Review of Psychology, 28, 1–39.CrossRefGoogle Scholar
Slovic, P. & Tversky, A. (1974). Who accepts Savage's axiom? Behavioral Science, 19, 368–373.CrossRefGoogle Scholar
Thomson, R.J. (2003). The use of utility functions for investment channel choice in defined- contribution retirement funds: Part II: A proposed system. British Actuarial Journal, 9, 903–958.CrossRefGoogle Scholar
Trowbridge, C.L. (1989). Fundamental concepts of actuarial science. Actuarial Education and Research Fund, Itasca.Google Scholar
Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.CrossRefGoogle Scholar
Tversky, A. (1975). On the elicitation of preferences: descriptive and normative preferences. Paper presented at the workshop on decision making with multiple conflicting objectives, Oct 1975, at International Institute for Applied Systems Analysis, Schloss Laxenburg, Austria.Google Scholar
Van der Waerden, B.L. (Ed.) (1975). Die werke van Jakob Bernoulli. Birkhaöser, Basel.Google Scholar
Von Mises, L. (1953). Human action. New Haven; cited in Kauder (1965: 117–118).Google Scholar
Von Neumann, J. & Morgenstern, O. (1947). Theory of games and economic behavior, 2nd ed. (1964). Wiley, New York.Google Scholar
Weber, M. (1951). Die Grenznutzlehre und das ‘psychophysische Grundgesetz’ in Gesammelte Aufsätze zur Wissenschaftslehre, 2nd ed., Tubingen,; cited in Kauder (1965: 117).Google Scholar
White, D.J & Brown, K. (Eds.) (1975). The role and effectiveness of theories of decision in practice. Hodder & Stoughton.Google Scholar
Yaari, M.E. (1987). The dual theory of choice under uncertainty. Econometrica, 55(1), 95–115.CrossRefGoogle Scholar