An Analysis Of The Nature Of Distortion Risk Measure

In our daily life, there is a lot of indeterminacy events which may bring about risks or benefits. We can use VaR or TVaR to measure the risk when we face the traditional risk,such as illness or traffic accident. And we will lack necessary date to construct a model when we face this kind of risks which have high claims and low frequency, such as earthquake and tsunamis. We apply the distortion risk measure to solve this kinds of problems. We can distort the tail distribution function of the risk to obtain the distortion risk measure.The second chapter of this thesis introduce the definition of risk and risk measure. We also give several properties to insure that we can get an excellent risk measure. Several problems have been introduced. The third chapter of this thesis introduce the definition of distortion function and distortion risk measure. The nature of distortion risk measure is introduced in this paper. When the risk random variable is discrete and negative, if the risk measure satisfies the properties of monotonicity, constancy and comonotonic additivity,there is a unique distorted function makes the risk measure can be expressed as the form of distortion risk measure. When the risk random variable is continuous and negative, if the risk measure satisfies the properties of monotonicity, constancy, comonotonic additivity and continuity, there is a unique distorted function makes the risk measure can be expressed as the form of distortion risk measure.