Journal
JOURNAL OF RISK AND UNCERTAINTY
Volume 44, Issue 3, Pages 243-260Publisher
SPRINGER
DOI: 10.1007/s11166-012-9141-9
Keywords
DARA; Downside risk; Downside risk aversion; Decreasing absolute risk aversion; Prudence
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Downside risk increases have previously been characterized as changes preferred by all decision makers u(x) with u'''(x) > 0. For risk averse decision makers, u'''(x) > 0 also defines prudence. This paper finds that downside risk increases can also be characterized as changes preferred by all decision makers displaying decreasing absolute risk aversion (DARA) since those changes involve random variables that have equal means. Building on these findings, the paper proposes using more decreasingly absolute risk averse or more prudent as alternative definitions of increased downside risk aversion. These alternative definitions generate a transitive ordering, while the existing definition based on a transformation function with a positive third derivative does not. Other properties of the new definitions of increased downside risk aversion are also presented.
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