Risk Measurement Strategy; An Alternative to Merging that Offers A Capital Relief in Risk Management

In this paper, we suggest the authenticity of a distortion risk measurement strategy that can be used instead of the risk management slogan Avoiding merging increases shortfall which justifies the well known advice dont put all your eggs in one basket. There are lots of distortion risk measures like conditional value at risk (expected shortfall) or the Wang transform risk measure, in spite of being coherent they do not always provide incentive for risk management because of lack of giving a capital relief in some simple two scenarios situation of reduced risk. To prevent the existence of such pathological counter examples, we introduce a Weibull distortion measure that preserves the higher degree stop loss order and offer a capital relief.