Measure Of Riskiness Based On RDEU Model

Facing unknown risk,it is difficult to make an immediate decision.Risk measure-ment as a effective tool is conducive to agents choosing the optimal behavior.Accurate risk measurement can greatly help investors to adjust their portfolios and avoid risks in order to achieve maximum returns.However,incorrect risk measurement is one of the main reasons for the bankruptcy of long-term capital company.Therefore,accurate risk measurement is of great significance.To accurately measuring risks,scholars quantify risks according to the objective distribution of risk assets,as risks are objectively existing uncertainties and possible losses.However,this method exists controversy.The risk is totally based on the distri-bution of a gamble about which one may doubt whether other take the gamble as serious as him.Couraged by constructing a risk measurement which combines distribution and feeling of agents,this paper proposes a subjective risk measurement of "gambles" which are general name of risk assets based on the RDEU model,which depends on both the gambling itself and the attitude of decision makers.At the same time,this measure applies to all bounded gambles,making it easier to compare different gambles.The probabilistic perception function in RDEU model is limited to the definition of distortion function,and the mathematical expectation obtained in this case is defined as the scale function in this paper.Further study found that when the scale function is 0,there is a unique true value,which we define as the risk based on the RDEU model.The research shows that the risk has good properties such as monotonicity,positive homogeneity,subdilution and continuity in a particular set.At the same time,we also apply the risk based on RDEU model to the actual comparison of risk aversion.The estimated risk value and the real risk value based on RDEU model are calculated by simulation,and it is found that the estimated value is close to the real value by comparison,which proves that the risk measurement is accurate and scientific,and can be well applied in real life.