Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model

By Alain Chateauneuf, M. Cohen, Isaac Meilijson. 2004

116 citations recorded by the source corpus.

This article presents various notions of risk generated by the intuitively appealing single-crossing operations between distribution functions. These stochastic orders, Bickel & Lehmann dispersion or (its equal-mean version) Quiggin's monotone mean-preserving increase in risk and Jewitt's location-independent risk, have proved to be useful in the study of Pareto allocations, ordering of insurance premia and other applications in the Expected Utility setup. These notions of risk are also relevant tothe Quiggin-Yaari Rank-dependent Expected Utility (RDEU) model of choice among lotteries. Risk aversion is modeled in the vNM Expected Utility model by Rothschild & Stiglitz's Mean Preserving Increase in Risk (MPIR). Realizing that in the broader rank-dependent set-up this order is too weak to classify choice, Quiggin developed the stronger monotone MPIR for this purpose. This paper reviews four notions of mean-preserving increase in risk - MPIR, monotoneMPIR and two versions of location-independent risk (renamed here left and right monotone MPIR) - and shows which choice questions are consistently modeled by each of these four orders.

Subfields: Economics and Econometrics, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/014696a3e7355df2036cd50de09ee3a9ac2da084

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Horst Zank
2. Alain Chateauneuf
3. Louis Eeckhoudt
4. Roger J. A. Laeven
5. Ulrich Schmidt
6. Han Bleichrodt

In General Decision Sciences

1. Horst Zank
2. Roger J. A. Laeven
3. Alain Chateauneuf
4. Ulrich Schmidt
5. Han Bleichrodt
6. Mohammed Abdellaoui

In Management Science and Operations Research

1. Alain Chateauneuf
2. Louis Eeckhoudt
3. Horst Zank
4. Roger J. A. Laeven
5. Ulrich Schmidt

Citations in the corpus

• The value of a Statistical Life under Ambiguity Aversion (2010, unknown): “) ‘‘star-shaped at 0’’ defined in [10].”
• What is Loss Aversion? (2005, background): “Hence, nonconcave utility may also coexist with aversion to monotone mean preserving spreads (see also Chateauneuf, Cohen, and Meilijson, 2004b; Abouda and Chateauneuf, 2002).”
• More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model (2005, background): “A forthcoming paper [9] analyzes other roles played by monotone risk and its weaker version Location-independent Risk by Jewitt, in the same model.”
• Risk Aversion in the Small and in the Large under Rank-Dependent Utility (2015, background): “For instance, in the dual theory (Yaari [17]) or under rank-dependent utility (Quiggin [11]), Yaari [16], Chew, Karni and Safra [4], Roëll [12], Chateauneuf, Cohen and Meilijson [3], and Ryan [13] have proposed ∗Corresponding author.”