具有双曲绝对风险厌恶函数类投资者的风险度量  

Making Calculated Estimation Risk Psychologically Acceptable to HARA-Function Type Investors and Raising its Precision and Stability

作　　者：张凌梅[1] 徐伟[1] 刘裕荷[1] 孟晓玲[1] 

机构地区：[1]西北工业大学理学院应用数学系,陕西西安710072

出　　处：《西北工业大学学报》2006年第6期741-744,共4页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10472091;10332030);陕西省自然科学基金(2003A03)资助

摘　　要：将风险厌恶函数与风险的度量有机的结合起来,给出了双曲绝对风险厌恶函数类投资者的一致性风险度量M,并使用最小方差外推法估计M。数值模拟的结果表明:在给定的置信水平下,用最小方差外推法估计的M比历史模拟法更稳定、更有效,且风险厌恶因子γ的引入使得M测量的风险值相对大小与投资者真实心理感受相符。Aim. Existing methods improved on VaR（Value-at-Risk）method. But, in our opinion, 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. In the full paper, we explain our new method in detail; in this abstract, we just add some pertinent remarks to listing the 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 Mφ（subtopic 1.1）; risk measure suitable for HARA-function type investor （subtopic 1. 2）, and estimation of function Mφ（subtopic 1. 3）; under topic 1 we give eqs. （1） through （9） ,the first four equations are taken from the open literature and the last five equations are derived by us ;under subtopic 1.2, we point out that eq. （5） includes the risk aversion factor γ, 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; under topic 2, eq. （10） is taken from the open literature. Finally we give a numerical simulation example, whose results are given in Tables 1 and 2 in the full paper. These results indicate preliminarily that our new method can raise the precision and stability of the calculated estimation risk.

关 键 词：双曲类绝对风险厌恶函数 一致性风险度量 最小方差外推法 

分 类 号：F830[经济管理—金融学]