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A two-parameter model of dispersion aversion. (English) Zbl 1295.91029
Summary: The idea of representing choice under uncertainty as a trade-off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of objective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the state-wise utility of an act. The dispersion measure exhibits positive linear homogeneity, sub-additivity, translation invariance and complementary symmetry. Since preferences are only weakly separable in terms of these two summary statistics, the uncertainty premium need not be constant. We generalize the concept of decreasing absolute risk aversion. Further we derive two-fund separation and asset pricing results analogous to those that hold for the standard CAPM.

91B06 Decision theory
91B25 Asset pricing models (MSC2010)
Full Text: DOI
[1] Anscombe, F. J.; Aumann, R. J., A definition of subjective probability, Ann. Math. Stat., 34, 199-205, (1963) · Zbl 0114.07204
[2] Baillon, A.; L╩╝Haridon, O.; Placido, L., Ambiguity models and the machina paradoxes, Amer. Econ. Rev., 101, 1547-1560, (2011)
[3] Chew, S.-H.; Sagi, J., Small worlds: modeling attitudes toward sources of uncertainty, J. Econ. Theory, 139, 1, 1-24, (2008) · Zbl 1132.91370
[4] Ellsberg, D., Risk, ambiguity and the savage axioms, Quart. J. Econ., 75, 643-669, (1961) · Zbl 1280.91045
[5] Epstein, L. G., Decreasing risk aversion and mean-variance analysis, Econometrica, 53, 945-961, (1985) · Zbl 0583.90008
[6] Ergin, H.; Gul, F., A theory of subjective compound lotteries, J. Econ. Theory, 144, 3, 899-929, (2009) · Zbl 1162.91331
[7] Fama, E. H.; Roll, R., Some properties of symmetric stable distributions, J. Amer. Statistical Assoc., 63, 817-836, (1968)
[8] Fishburn, P. C., Utility theory for decision making, (1970), Wiley New York · Zbl 0213.46202
[9] French, K.; Poterba, J., Investor diversification and international equity markets, Amer. Econ. Rev., 81, 222-226, (1991)
[10] Ghirardato, P.; Maccheroni, F., Ambiguity made precise: A comparative foundation, J. Econ. Theory, 102, 251-289, (2002) · Zbl 1019.91015
[11] Gilboa I, I.; Schmeidler, D., Maxmin expected utility with a non-unique prior, J. Math. Econ., 18, 141-153, (1989) · Zbl 0675.90012
[12] Grant, S.; Polak, B., Mean-dispersion preferences and constant absolute uncertainty aversion, J. Econ. Theory, 148, 1361-1398, (2013) · Zbl 1285.91033
[13] Hansen, I. N.; Sargent, T., Robust control and model uncertainty, Amer. Econ. Rev., 91, 60-66, (2001)
[14] Lintner, J., The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Rev. Econ. Statist., 47, 13-37, (1965)
[15] Maccheroni, F.; Marinacci, M.; Rustichini, A., Dynamic variational preferences, J. Econ. Theory, 128, 4-44, (2006) · Zbl 1153.91384
[16] Machina, M., Risk, ambiguity and the rank-dependence axioms, Amer. Econ. Rev., 99, 745-780, (2009)
[17] Machina, M.; Schmeidler, D., A more robust definition of subjective probability, Econometrica, 60, 745-780, (1992) · Zbl 0763.90012
[18] Markowitz, H., Portfolio selection, J. Finance, 7, 77-91, (1952)
[19] Quiggin, J.; Chambers, R. G., Invariant risk attitudes, J. Econ. Theory, 117, 96-118, (2004) · Zbl 1086.91037
[20] Rockafellar, R. T.; Uryasev, S.; Zabarankin, M., Generalized deviations in risk analysis, Finance Stochastics, 10, 51-74, (2006) · Zbl 1150.90006
[21] Savage, L. J., Foundations of statistics, (1954), Wiley New York · Zbl 0121.13603
[22] Sharpe, W., Capital asset prices: A theory of market equilibrium under conditions of risk, J. Finance, 19, 425-442, (1964)
[23] Siniscalchi, M., Vector expected utility and attitudes toward variation, Econometrica, 77, 3, 801-855, (2009) · Zbl 1182.91061
[24] Tobin, J., Liquidity preference as behavior toward risk, Rev. Econ. Stud., 25, 65-86, (1958)
[25] Wang, X.; Wen, Z.; Huang, Z., A capital asset pricing model under stable Paretian distributions in a pure exchange economy, Acta Math. Appl. Sin. Engl. Ser., 20, 675-684, (2004) · Zbl 1138.91484
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