×

zbMATH — the first resource for mathematics

Higher-order generalizations of Arrow-Pratt and Ross risk aversion: a comparative statics approach. (English) Zbl 1281.91101
Summary: We analyze comparative risk aversion in a new way, through a comparative statics problem in which, for a cost, agents can shift from an initial probability distribution toward a preferred distribution. The Ross characterization arises when the original distribution is riskier than the preferred distribution and the cost is monetary, and the Arrow-Pratt characterization arises when the original distribution differs from the preferred distribution by a simple mean-preserving spread and the cost is a utility cost. Higher-order increases in risk lead to higher-order generalizations, and the comparative statics method yields a unified approach to the problem of comparative risk attitudes.

MSC:
91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arrow, K.J., Essays in the theory of risk-baring, (1974), Markham Chicago, IL · Zbl 0323.90014
[2] Bigelow, J.P.; Menezes, C.F., Outside risk aversion and the comparative statics of increasing risk in quasi-linear decision models, Int. econ. rev., 36, 643-673, (1995) · Zbl 0836.90001
[3] Briys, E.; Schlesinger, H., Risk aversion and propensities for self-insurance and self-protection, Southern econ. J., 57, 458-467, (1990)
[4] Caballe, J.; Pomansky, A., Mixed risk aversion, J. econ. theory, 71, 485-513, (1996) · Zbl 0877.90009
[5] Chiu, W.H., Degree of downside risk aversion and self-protection, Ins.: mathematics econ., 36, 93-101, (2005) · Zbl 1111.91022
[6] Chiu, W.H., Skewness preference, risk aversion, and the precedence relations on stochastic changes, Manage. sci., 51, 1816-1828, (2005)
[7] Dionne, G.; Eeckhoudt, L., Self-insurance, self-protection and increased risk aversion, Econ. letters, 17, 39-42, (1985) · Zbl 1273.91235
[8] Eeckhoudt, L.; Schlesinger, H., Putting risk in its proper place, Amer. econ. rev., 96, 280-289, (2006)
[9] Ehrlich, I.; Becker, G.S., Market insurance, self-insurance, and self-protection, J. polit. econ., 80, 623-648, (1972)
[10] Ekern, S., Increasing \(N\)th degree risk, Econ. letters, 6, 329-333, (1980)
[11] Kimball, M.S., Precautionary saving in the small and in the large, Econometrica, 58, 53-73, (1990)
[12] Machina, M.J., Comparative statistics and non-expected utility preferences, J. econ. theory, 47, 393-405, (1989) · Zbl 0683.90010
[13] Machina, M.J.; Neilson, W.S., The ross characterization of risk aversion: strengthening and extension, Econometrica, 55, 1139-1149, (1987) · Zbl 0635.90010
[14] Menezes, C.F.; Geiss, C.; Tressler, J., Increasing downside risk, Amer. econ. rev., 70, 921-932, (1980)
[15] Menezes, C.F.; Wang, X.H., Increasing outer risk, J. math. econ., 41, 875-886, (2005) · Zbl 1117.91382
[16] Meyer, J.; Ormiston, M.B., The comparative statics of cumulative distribution function changes for the class of risk averse agents, J. econ. theory, 31, 153-169, (1983) · Zbl 0519.90005
[17] Modica, S.; Scarsini, M., A note on comparative downside risk aversion, J. econ. theory, 122, 267-271, (2005) · Zbl 1114.91063
[18] Pratt, J.W., Risk aversion in the small and in the large, Econometrica, 32, 122-136, (1964) · Zbl 0132.13906
[19] Ross, S.A., Some stronger measures of risk aversion in the small and in the large with applications, Econometrica, 49, 621-663, (1981) · Zbl 0471.90016
[20] Rothschild, M.; Stiglitz, J.E., Increasing risk: I. A definition, J. econ. theory, 2, 225-243, (1970)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.