Comparative risk apportionment
Tóm tắt
A decision maker who would rather apportion an independent risk in a state with a good lottery than in a state with a bad lottery is said to have a preference for risk apportionment (Eeckhoudt and Schlesinger in Am Econ Rev 96:280–289, 2006). In this paper, we propose a measure for the strength of nth-degree risk apportionment preference based on Pratt’s probability premium (Pratt in Econometrica 32:122–136, 1964). Under expected utility theory, we analyze the relationship between a greater preference for risk apportionment and both the Ross and Arrow–Pratt versions of comparative risk aversion.
Tài liệu tham khảo
Arrow, K.J.: Essays in the Theory of Risk-Bearing. Markham, Chicago (1971)
Bernoulli, D.: Exposition of a new theory on the measurement of risk. Econometrica 22, 23–36 (1954)
Cabellé, J., Pomansky, A.: Mixed risk aversion. J. Econ. Theory 71, 485–513 (1996)
Chiu, W.H.: Degree of downside risk aversion and self-protection. Insur. Math. Econ. 36, 93–101 (2005)
Chiu, W.H., Eeckhoudt, L., Rey, B.: On relative and partial risk attitudes: theory and implications. Econ. Theory 50, 151–167 (2012)
Crainich, D., Eeckhoudt, L.: On the intensity of downside risk aversion. J. Risk Uncertain. 36, 267–276 (2008)
Crainich, D., Eeckhoudt, L.: Three measures of the intensity of temperance. IESEG School of Management Working Paper (2011)
Crainich, D., Eeckhoudt, L., Trannoy, A.: Even (mixed) risk lovers are prudent. Am. Econ. Rev. 103, 1529–1535 (2013)
Crainich, D., Eeckhoudt, L., Le Courtois, O.: Intensity of preferences for bivariate risk apportionment. J. Math. Econ. 88, 153–160 (2020)
Denuit, M., Eeckhoudt, L.: Stronger measures of higher-order risk attitudes. J. Econ. Theory 145, 2027–2036 (2010)
Denuit, M., Rey, B.: Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes. Math. Soc. Sci. 60, 137–143 (2010)
Denuit, M., Rey, B.: Another look at risk apportionment. J. Math. Econ. 49, 335–343 (2013)
Ebert, S.: Even (mixed) risk lovers are prudent: comment. Am. Econ. Rev. 103, 1536–1537 (2013)
Ebert, S., Wiesen, D.: Joint measurement of risk aversion, prudence, and temperance. J. Risk Uncertain. 48, 231–252 (2014)
Ebert, S., Nocetti, D.C., Schlesinger, H.: Greater mutual aggravation. Manag. Sci. 64, 2809–2811 (2018)
Eeckhoudt, L.: Beyond risk aversion: why, how and what’s next? Geneva Risk Insur. Rev. 37, 141–155 (2012)
Eeckhoudt, L., Schlesinger, H.: Putting risk in its proper place. Am. Econ. Rev. 96, 280–289 (2006)
Eeckhoudt, L., Schlesinger, H.: On the utility premium of Friedman and Savage. Econ. Lett. 105, 46–48 (2009)
Eeckhoudt, L., Schlesinger, H., Tsetlin, I.: Apportioning of risks via stochastic dominance. J. Econ. Theory 144, 994–1003 (2009)
Eeckhoudt, L., Laeven, R.J.A., Schlesinger, H.: Risk apportionment: the dual story. J. Econ. Theory 185, 104971 (2020)
Ekern, S.: Increasing Nth degree risk. Econ. Lett. 6, 329–333 (1980)
Gollier, C.: A general theory of risk apportionment. Toulouse School of Economics Working Paper No. 19-1003 (2019)
Gollier, C., Pratt, J.W.: Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109–1123 (1996)
Huang, R.J., Tzeng, L.Y., Zhao, L.: Fractional degree stochastic dominance. Manag. Sci. 66, 4630–4647 (2020)
Jindapon, P.: Prudence probability premium. Econ. Lett. 109, 34–37 (2010)
Jindapon, P., Neilson, W.S.: Higher-order generalizations of Arrow–Pratt and Ross risk aversion: a comparative statics approach. J. Econ. Theory 136, 719–728 (2007)
Jokung, O.: Risk apportionment via bivariate stochastic dominance. J. Math. Econ. 47, 448–452 (2011)
Keenan, D.C., Snow, A.: Greater downside risk aversion. J. Risk Uncertain. 24, 267–277 (2002)
Keenan, D.C., Snow, A.: The Schwarzian derivative as a ranking of downside risk aversion. J. Risk Uncertain. 44, 149–160 (2012)
Kimball, M.S.: Precautionary saving in the small and in the large. Econometrica 58, 53–73 (1990)
Kimball, M.S.: Standard risk aversion. Econometrica 61, 589–611 (1993)
Li, J.: Comparative higher-degree Ross risk aversion. Insur. Math. Econ. 45, 333–336 (2009)
Li, J., Liu, L.: The monetary utility premium and interpersonal comparisons. Econ. Lett. 125, 257–260 (2014)
Liu, L., Meyer, J.: Decreasing absolute risk aversion, prudence and increased downside risk aversion. J. Risk Uncertain. 44, 243–260 (2012)
Liu, L., Meyer, J.: Substituting one risk increase for another: a method for measuring risk aversion. J. Econ. Theory 148, 2706–2718 (2013)
Liu, L., Neilson, W.S.: Alternative approaches to comparative \(n\)th-degree risk aversion. Manag. Sci. 65, 3824–3834 (2019)
Machina, M.J., Neilson, W.S.: The Ross characterization of risk aversion: strengthening and extension. Econometrica 55, 1139–1149 (1987)
Menegatti, M.: The risk premium and the effects of risk on agents utility. Res. Econ. 65(2), 89–94 (2011)
Menegatti, M., Peter, R.: Risk effects on optimal decision making: a question of the right order (2020). http://dx.doi.org/10.2139/ssrn.3585380
Menezes, C., Wang, X.H.: Increasing outer risk. J. Math. Econ. 41, 875–886 (2005)
Menezes, C., Geiss, C., Tressler, J.: Increasing downside risk. Am. Econ. Rev. 70, 921–932 (1980)
Modica, S., Scarsini, M.: A note on comparative downside risk aversion. J. Econ. Theory 122, 267–271 (2005)
Nocetti, D.: Robust comparative statics of risk changes. Manag. Sci. 62, 1381–1392 (2016)
Peter, R.: Who should exert more effort? Risk aversion, downside risk aversion and optimal prevention. Econ. Theory (2020). https://doi.org/10.1007/s00199-020-01282-0
Pratt, J.W.: Risk aversion in the small and in the large. Econometrica 32, 122–136 (1964)
Pratt, J.W., Zeckhouser, R.J.: Proper risk aversion. Econometrica 55, 143–154 (1987)
Ross, S.A.: Some stronger measures of risk aversion in the small and in the large with applications. Econometrica 49, 621–663 (1981)
Rothschild, M., Stiglitz, J.: Increasing risk I: a definition. J. Econ. Theory 2, 225–243 (1970)
Tsetlin, I., Winkler, R.L.: Multiattribute utility satisfying a preference for combining good with bad. Manag. Sci. 55, 1942–1952 (2009)
Tsetlin, I., Winkler, R.L.: Multivariate almost stochastic dominance. J. Risk Insur. 85, 431–445 (2018)
Wang, J., Li, J.: Multiplicative risk apportionment. Math. Soc. Sci. 60, 79–81 (2010)
Watt, R.: A note on greater downside risk aversion. International Center for Economic Research Working Paper No. 17/2011 (2011)