Abstract
In a recent article entitled “Putting Risk in its Proper Place,” Eeckhoudt and Schlesinger (2006) established a theorem linking the sign of the n-th derivative of an agent’s utility function to her preferences among pairs of simple lotteries. We characterize these lotteries and show that, in a given pair, they only differ by their moments of order greater than or equal to n. When the n-th derivative of the utility function is positive (negative) and n is odd (even), the agent prefers a lottery with higher (lower) n + 2p-th moments for p belonging to the set of positive integers. This result links the preference for disaggregation of risks across states of nature to the complete structure of moments preferred by mixed risk averse agents. It can be viewed as a generalization of a proposition appearing in Ekern (1980) which focused only on the differences in the n-th moments.
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References
Brockett P. L., Kahane Y. (1992) Risk, return, skewness and preference. Management Science 38(6): 851–866
Caballé J., Pomansky A. (1996) Mixed risk aversion. Journal of Economic Theory 71(2): 485–513
Chiu, W. H. (2008). Skewness preference, risk taking and expected utility maximization. Working Paper. University of Manchester.
Deck, C. A., & Schlesinger, H. (2008). Exploring higher-order risk effects. CESifo Working Paper Series 2487 (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1313032).
Eeckhoudt L., Gollier C., Schneider T. (1995) Risk-aversion, prudence and temperance: A unified approach. Economics Letters 48(3–4): 331–336
Eeckhoudt L., Schlesinger H. (2006) Putting risk in its proper place. American Economic Review 96: 280–289
Ekern S. (1980) Increasing N-th degree risk. Economics Letters 6: 329–333
Kimball M. S. (1990) Precautionary savings in the small and in the large. Econometrica 58: 53–73
Kimball M. S. (1992). Precautionary motives for holding assets. In: Newman P., Milgate M., Falwell J. (Eds) New Palgrave dictionary of money and finance (Vol. 3). London, MacMillan, pp 158–161
Kimball M. S. (1993) Standard risk aversion. Econometrica 61(3): 589–611
Lajeri-Chaherli F. (2004) Proper prudence, standard prudence and precautionary vulnerability. Economic Letters 82: 29–34
Menezes C., Geiss C., Tressler J. (1980) Increasing downside risk. American Economic Review 70: 921–932
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Roger, P. Mixed risk aversion and preference for risk disaggregation: a story of moments. Theory Decis 70, 27–44 (2011). https://doi.org/10.1007/s11238-009-9176-9
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DOI: https://doi.org/10.1007/s11238-009-9176-9