A Study For The Measurement Of The Risk Of Security Investment And Its Applications

All the investors in the security market hope to find the best assets or portfolio so as to get the highest utility, or the largest extent of satisfaction. As is known to all, almost every asset has an uncertain return, which results in an uncertain utility to the investors, and that is where the risk comes from. So the investors have to weigh between the two most significant factors which influence the utility of the asset---the expected return and the risk in order to gain the highest utility. The focus of the thesis is how to measure and control the risk of the security risk and how to measure the utility investors gain from the assets.On the basis of the traditional methods to measure the risk of security investment, we discuss information entropy--- another method to measure the risk of security investment as well as its properties and its relations and differences to variance---the classical method to measure the risk of security investment. Then, we introduce behavioral portfolio theory and how to measure the perceptional risk of irrational investors。Furthermore, we focus on the information entropy of the return of the portfolio on condition that the joint distribution of the return of each asset is a multivariate normal distribution, a multivariate t distribution and a multivariate (piecewise) uniform distribution and the respective optimization model, and we use the multivariate (piecewise) uniform distribution to approximate a multivariate continuous distribution in order to get the approximate optimal portfolio weight on condition that the returns of the assets are independent to each other and the distribution of each asset is a multivariate continuous distribution. Finally, we introduce the fuzzy environment and discuss how to select the portfolio weight so as to maximize the integrated utility of the expectation and risk of the return of the portfolio for investors with different attitudes to the risk on the fuzzy environment and use the models in empirical analysis.