Comparative risk aversion vs. threshold choice in the Omega ratio
研究了Omega比率中的阈值参数能否代表风险厌恶，通过推导风险溢价渐近展开，发现当附加风险方差随背景风险递减且背景风险密度对数凹时，阈值具有单调性，否则不能代表风险厌恶。
We study conditions under which the threshold parameter in the Omega ratio represents risk aversion in the sense of monotonicity of risk premia. To this end, we derive asymptotic expansions for risk premia associated with taking a small additional risk on top of a background risk. These risk premia have the expected monotonicity behavior if, roughly speaking, the variance of the additional risk decreases with the background risk and if the density of the background risk is log-concave. When these conditions are violated, the threshold in the Omega ratio does not represent risk aversion in general. Finally, we compare our sufficient conditions for the Omega ratio to those that are needed to guarantee monotonicity of risk premia with an expected utility criterion under background risk. We argue that the conditions that are needed for the Omega threshold to represent risk aversion are comparable to those that are needed for expected utility with exponential utility functions.