A class of non-expected utility risk measures and implications for asset allocations

This paper discusses a class of risk measures developed from a risk measure recently proposed for insurance pricing. This paper reviews the distortion function approach developed in the actuarial literature for insurance risk. The proportional hazards transform is a particular case. The relationship between this approach to risk and other approaches including the dual theory of choice under risk is discussed. A new class of risk measures with suitable properties for asset allocation based on the distortion function approach to insurance risk is developed. This measure treats upside and downside risk differently. Properties of special cases of the risk measure and links to conventional portfolio selection risk measures are discussed.