The Study Of Distortion Risk Measure In Skewed Normal Distribution

Narrowly, the portfolio theory investigates how to select and allocate assets on the target of a portfolio is to make the return of the portfolio maximized in a given risk level or to’make the risk of the portfolio minimized in a given level of return. So, the risk measure is crucial in the construction of a portfolio. Different risk measures will result in a different portfolio. For recent years, influenced by the factors of global economic integration, financial innovation and so on, there are many huge changes taking place in the financial market, and risks become more and more complicated. In the field of financial economics, there are many risk measures, such as Variance, VaR (value at risk), CVaR (Conditional Value at Risk) and so on. These risk measurement method has different features. VaR (value at risk) shows the worst loss at a minimum number of losses and the probability of occurrence in a loss. It is easy to understand and so widely used. CVaR reflects average loss beyond points VaR, it in the depiction and measure risk; it have an advantage more than VaR; and it is a coherent risk measure. However, they all have major defects:those measures don’t considerate all the information of the initial distribution, ignoring high-risk events. Although these extreme tail risks occur infrequently, it might create significant impact on investors, regulators if the event occurs.Risks management is a hot topic in financial community, academic, and financial supervisors. So, the research and development of risk measurement is significantly important. Among them, the small probability of extreme high numerical tail risk events calls people’s attention. making accurate judgment and prognosticate to these tail extreme events, we need to find a more suitable model which deals with these extreme cases. Wang (2000) put forward Wang’s transform which is the source of distortion risk measure. This type of risk measures in essence emphasizes the tail risk, which give a greater weight to high-risk events through modifying the distribution, which makes full use of loss distribution and effectively measure tail risk. The two type of Wang’s transform are under the assumption that the risk is normally distribution or t-distribution. In this paper. modifying Wang’s transform with inverse scale factor skew-normal distribution, get a new distortion function, and the risk measure defined by Choquet integral is proved to be coherent. The article divides into following sections.The first part introduces this problem, and the purpose of the research and the structure, and the disadvantages.The second part introduces portfolio theory and risk measures, such as variance, VaR and so on. This section introduces those risk measures’merit and demerit.The third part introduces coherent risk measurers, and CVaR including of the concept, method of calculation. Finally points out that the defects of CVaR.The fourth part introduces the concept, character of distortion risk measure, And points out the demerit of two type of Wang’s transform which are under the assumption that the risk is normally distribution or t-distribution.The fifth part introduces a new version of Wang’s transform with inverse scale factor skew-normal distribution. This section introduces a new distortion function is based on a skew-normal distribution, the risk measure defined by Choquet integral is proved to be coherent. Moreover we study the portfolio optimization problem under the assumption that the risk is normally distributed.The sixth part selects5stocks as samples to research and analyze the results of portfolio optimal under distortion risk measure.Finally is the conclusion. This part puts forward the research conclusion and some problems in this paper.This feature of the paper:introducing a new distortion function is based on a skew-normal distribution, and proved it is coherent. Research and analyze the results of portfolio optimal under distortion risk measure by samples.The lack of major steps:Fist, this paper has not given the effectiveness inspection of the distorted risk measure.Second, for the selection of parameters, this paper also gives no reasonable interval. Third, this paper just analyzes the distortion risk measure in portfolio optimal solution when loss distribution is normal.