Based On Spectral Risk Measure Of Portfolio Problems

Since VaR method is absent of general subadditivity and description to tail information, a new risk measure framework is proposed in recent years, it is coherent risk measure. Under this framework, many risk measure technologies are established, one of which is the spectral risk measure. It grows from Expected Shortfall and generalizes Expected Shortfall. At the same time, the spectral risk measure is one kind of coherent risk measures. The spectral risk measure combines the distribution of profit and loss with the subjective risk aversion from the investors. It provides an available choice in measuring risk properly and effectively.This paper studies the portfolio problems on the basis of the spectral risk measure and gets some useful results.First of all, under the assumption of normality of risk securities this paper discusses the mean-spectral risk measure efficient frontier of portfolio and gets an analytical formula. The comparison between the mean-variance efficient frontier and the mean-spectral risk measure efficient frontier is provided by virtue of theory and examples.Secondly, from the fact of investor decision, the author gives a portfolio model with spectral risk measure constraints, and takes an example to check the efficiency of this model.