Spectral risk measures base on risk spectrum function

A hyperbolic absolute risk aversion(HARA) spectrum function is proposed and an estimation of spectral risk measures with the HARA spectrum function,backing tests and the portfolio optimization model is obtained.The empirical analysis shows that the hyperbolic spectral risk measure of a single asset is affected by the confidence level and risk aversion factor,while the optimal allocation of the portfolio based on the hyperbolic spectral risk measures is influenced by the expected rate of return and risk aversion factor.