zbMATH — the first resource for mathematics

On the intensity of downside risk aversion. (English) Zbl 1151.91428
Summary: The degree of downside risk aversion (or equivalently prudence) is so far usually measured by $$\frac{-U^{\prime \prime \prime}}{U^{\prime \prime}}$$. We propose here another measure, $$\frac{U^{\prime \prime \prime}}{U^{\prime}}$$, which has specific and interesting local and global properties. Some of these properties are to a wide extent similar to those of the classical measure of absolute risk aversion, which is not always the case for $$\frac{-U^{\prime \prime \prime}}{U^{\prime \prime}}$$. It also appears that the two measures are not mutually exclusive. Instead, they seem to be rather complementary as shown through an economic application dealing with a simple general equilibrium model of savings.

MSC:
 91B16 Utility theory
Full Text:
References:
 [1] Aumann, Robert and Mordecai Kurz. (1977). ”Power and Taxes,” Econometrica 45(5), 1137–1161. · Zbl 0367.90016 [2] Arrow, Kenneth. (1965). Aspects of the Theory of Risk-bearing. Helsinki: Yrjš Jahnsson Foundation. [3] Barsky, Robert. (1989). ”Why Don’t the Prices of Stocks and Bonds Move Together?” American Economic Review 79, 1132–1145. [4] Diamond, Peter and Joseph Stiglitz. (1974). ”Increases in Risk and in Risk Aversion,” Journal of Economic Theory 8(3), 335–360. [5] Eeckhoudt, Louis and Harris Schlesinger. (2006). ”Putting Risk in its Proper Place,” American Economic Review 96(1), 280–289. [6] Eeckhoudt, Louis and Harris Schlesinger. (1994). ”A Precautionary Tale of Risk Aversion and Prudence.” In B. Munier and M. Machina (eds), Models and Experiments in Risk and Rationality 75–90, Dordrecht: Kluwer Academic Publishers. · Zbl 0860.90038 [7] Foncel, Jérôme and Nicolas Treich. (2005). ”Fear of Ruin,” The Journal of Risk and Uncertainty 31(3), 289–300. · Zbl 1125.91364 [8] Friedman, Milton and Leonard Savage. (1948). ”The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56(4), 279–304. [9] Gollier, Christian and John Pratt. (1996). ”Risk Vulnerability and the Tempering Effect of Background Risk,” Econometrica 64(5), 1109–1123. · Zbl 0856.90014 [10] Jindapon, Paan and William Neilson. (2007). ”Higher-order Generalizations of Arrow–Pratt and Ross Risk Aversion: A Comparative Statics Approach,” Journal of Economic Theory 136(1), 719–728. · Zbl 1281.91101 [11] Keenan, Donald and Arthur Snow. (2005). ”Greater Downside Risk Aversion,” The Journal of Risk and Uncertainty 24(3), 267–277. · Zbl 1005.91080 [12] Kimball, Miles. (1990). ”Precautionary Saving in the Small and in the Large,” Econometrica 58(1), 53–73. [13] Modica, Salvatore and Marco Scarsini. (2005). ”A Note on Comparative Downside Risk Aversion,” Journal of Economic Theory 122, 267–271. · Zbl 1114.91063 [14] Menezes, Carmen, C. Geiss and John Tressler. (1980). ”Increasing Downside Risk,” American Economic Review 70(5), 921–932. [15] Pratt, John. (1964). ”Risk Aversion in the Small and in the Large,” Econometrica 32, 122–136. · Zbl 0132.13906 [16] Ross, Stephen. (1981). ”Some Stronger Measures of Risk Aversion in the Small and the Large with Applications,” Econometrica 49(3), 621–638. · Zbl 0471.90016 [17] Scott, Robert and Philip Horvath. (1980). ”On the Direction of Preference for Moments of Higher Order than the Variance,” The Journal of Finance 35(4), 915–919.
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.