Department of Mathematics, University of Leicester, LE1 7RH, UK.
Risk Anal. 2012 Aug;32(8):1277-92. doi: 10.1111/j.1539-6924.2011.01611.x. Epub 2011 Apr 7.
Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered.
均值-离差分析，以及连贯风险测度的现有理论和对偶效用理论，在不确定性下的选择理论的背景下进行了研究。该理论基于不同的公理，如传递性、单调性、连续性等，研究了对随机结果的理性偏好关系。连贯风险测度理论的公理基础是对偶效用理论公理的放松，进一步放松公理则导致了均值-离差分析。讨论了这些理论对应的公理集所产生的悖论及其可能的解决方法，并考虑了均值-离差分析在理性选择背景下的最优风险分担和投资组合选择中的应用。
