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Theory and Decision

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01.02.2014

Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance

verfasst von: Michel Denuit, Liqun Liu

Erschienen in: Theory and Decision | Ausgabe 2/2014

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Abstract

Fishburn and Vickson (Stochastic dominance: an approach to decision-making under risk, Lexington Books, D.C. Heath and Company, Lexington, pp. 39–113, 1978) showed that, when applied to random alternatives with an equal mean, 3rd-degree and decreasing absolute risk aversion stochastic dominances represent equivalent rules. The present paper generalizes this result to higher degrees. Specifically, higher-degree stochastic dominance rules and common preference by all decision makers with decreasing higher-order absolute risk aversion are shown to coincide under appropriate constraints on the respective moments of the random variables to be compared.

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This intuition is based on an alternative proof of the Fishburn and Vickson theorem in Liu and Meyer (2012a).

For example, Menezes et al. (1980) defined a third-degree or downside risk increase as a change in a random variable that moves risk from right to left while keeping the mean and variance intact. And Ekern (1980) defined an \(n\)th-degree risk increase as an \(n\)th-degree stochastically dominated change in a random variable that keeps the first \(n-1\) moments the same.

These lotteries were characterized by Roger (2011) who established that they only differ by their moments of order greater than or equal to \(n\). See also Ebert (2013).

Notice that we impose here a strict inequality to define risk apportionment, to avoid dividing by zero when defining \(A_{u,n,m}\) as ratios of derivatives of the utility function \(u\).

Arrow, K. J. (1971). Essays in the theory of risk-bearing. New York: North-Holland.

Brockett, P. L., & Golden, L. L. (1987). A class of utility functions containing all the common utility functions. Management Science, 33, 955–964.CrossRef

Caballe, J., & Pomansky, A. (1996). Mixed risk aversion. Journal of Economic Theory, 71, 485–513.CrossRef

Chiu, H. W. (2005). Skewness preference, risk aversion and the precedence relations on stochastic changes. Management Science, 51, 1816–1828.CrossRef

Denuit, M., & Eeckhoudt, L. (2010a). A general index of absolute risk attitude. Management Science, 56, 712–715.CrossRef

Denuit, M., & Eeckhoudt, L. (2010b). Stronger measures of higher-order risk attitudes. Journal of Economic Theory, 145, 2027–2036.CrossRef

Denuit, M., & Eeckhoudt, L. (2012). Risk attitudes and the value of risk transformations. International Journal of Economic Theory, in press.

Denuit, M., & Eeckhoudt, L. (2013). Improving your chances: A new result. Economics Letters, 118, 475–477.CrossRef

Denuit, M., Lefevre, C., & Scarsini, M. (2001). On s-convexity and risk aversion. Theory and Decision, 50, 239–248.CrossRef

Denuit, M., & Rey, B. (2010). Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes. Mathematical Social Sciences, 60, 137–143.CrossRef

Ebert, S. (2013). Moment characterization of higher-order risk preferences. Theory and Decision, 74, 267–284.CrossRef

Eeckhoudt, L., & Schlesinger, H. (2006). Putting risk in its proper place. American Economic Review, 96, 280–289.CrossRef

Eeckhoudt, L., & Schlesinger, H. (2009). On the utility premium of Friedman and Savage. Economics Letters, 105, 46–48.CrossRef

Eeckhoudt, L., Schlesinger, H., & Tsetlin, I. (2009). Apportioning of risks via stochastic dominance. Journal of Economic Theory, 144, 994–1003.CrossRef

Ekern, S. (1980). Increasing \(n\)th degree risk. Economics Letters, 6, 329–333.CrossRef

Fishburn, P., & Vickson, R. (1978). Theoretical foundations of stochastic dominance. In G. Whitmore & M. Findlay (Eds.), Stochastic dominance: An approach to decision-making under risk (pp. 39–113). Lexington, MA: Lexington Books, D.C. Heath and Company.

Kimball, M. S. (1990). Precautionary savings in the small and in the large. Econometrica, 58, 53–73.CrossRef

Kimball, M. S. (1992). Precautionary motives for holding assets. In P. Newman, M. Milgate, & J. Eatwell (Eds.), The new Palgrave dictionary of money and finance (Vol. 3, pp. 158–161). London: McMillan.

Liu, L., & Meyer, J. (2012a). Decreasing absolute risk aversion, prudence and increased downside risk aversion. Journal of Risk and Uncertainty, 44, 243–260.CrossRef

Liu, L., & Meyer, J. (2012b). Risk aversion orders and intensity measures of a higher degree. Working paper available at http://perc.tamu.edu/perc/Publication/workingpapers/1203.pdf.

Menezes, C., Geiss, C., & Tressler, J. (1980). Increasing downside risk. American Economic Review, 70, 921–932.

Menezes, C. F., & Wang, H. (2005). Increasing outer risk. Journal of Mathematical Economics, 41, 875–886.CrossRef

Pratt, J. W. (1964). Risk aversion in the small and in the large. Econometrica, 32, 122–136.CrossRef

Roger, P. (2011). Mixed risk aversion and preference for risk disaggregation: A story of moments. Theory and Decision, 70, 27–44.CrossRef

Rothschild, M., & Stiglitz, J. E. (1970). Increasing risk: I. A definition. Journal of Economic Theory, 2, 225–243.CrossRef

Titel: Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance
verfasst von: Michel Denuit
Liqun Liu
Publikationsdatum: 01.02.2014
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 2/2014
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9374-3

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