Research Of Spectral Risk Measure Based On Risk Attitude

Spectral risk measure is a kind of risk measurement which is researched gradually in-depth and used maturely in recent years. This is investors’ risk attitudes play a non-ignorable role on the accuracy of risk measurement.In this paper, we first summarize the recent study of several classical methods of dealing with risk measure and the advantages and disadvantages of their applications in theory, computation and practice. In addition, we introduce theories related to the risk attitude, such as utility function theory and distortion function theory. Based on these theories and some results gained before by others, we find a method to fully integrate risk attitudes into spectral risk measure.Finally, depending on different kinds of risk investors, we construct different spectral risk functions and make empirical analysis by applying the spectral risk measures constructed into investment portfolio and arbitrage portfolio. The result of the analysis in investment portfolio implies that the allocations of portfolio assets change with the risk attitudes. This result expresses that the spectral risk measures take the risk attitudes of the investors fully into account, so that the choices made in investment portfolio can correspond to the willing of the investors very well. The result of the analysis in arbitrage portfolio implies that the risk measures not only adhere the advantages of classical Va R, but also make up for its shortages, such as dissatisfying the principle of dispersing risk and underestimating risk.The main results are as following.Firstly, we find and summarize the drawbacks of existing methods constructing spectral risk functions by expected utility function and its inspiration. By virtue of distortion function, we make the connection of expected utility function theory and spectral risk measure. Based on this, we define risk aversion coefficient expressed by spectral risk function, which corresponds to the economic meaning of Arrow-Pratt.Secondly, for some kinds of frequently-used expected utility functions, by translation and dilation transforms, we find the distortion functions corresponding to their maximal terms, based on which we construct the corresponding spectral risk functions.Thirdly, we consider investors with changing risk attitudes and take those whose risk attitudes change with the expected yield for example. Given expected utility functions, we construct the mixed spectral risk measure model by means of the concavity and convexity and the corresponding distortion functions.Finally, we make empirical analysis of the models and conclusions supported in this paper by applying them to stocks and future contacts which are representative in China securities market and future market.