Making calculated estimation risk psychologically acceptable to HARA-function type investors and raising its precision and stability

Existing methods improved on VaR (Value-at-Risk)method. But their results are not acceptable psychologically to HARA (Hyperbolic Absolute Risk Aversion)-Function type investors. We now present what we believe to be a better method that can not only make our calculated estimation risk acceptable to such investors but also raise its precision and stability. We propose two topics of explanation: (1) risk measure suitable for HARA-function type investors; (2) least squares extrapolation method; the three subtopics of topic 1 are ES (expected shortfall) and the concept of coherent spectral risk measure function M_φ; risk measure suitable for HARA-function type investor, and estimation of function M_φ. We point out that eq. (5) includes the risk aversion factor 7, which can be selected by the investors and such selection is the important reason why the calculated estimation risk is psychologically acceptable to the investor. Finally we give a numerical simulation example and the results indicate preliminarily that our new method can raise the precision and stability of the calculated estimation risk.