Research And Application Of Entropy Theory In Portfolio Investment Decision

The main wish of investors is to obtain maximum profits for themselves. Since invest return is tightly associated with the risk, the commonsense principle is that the investors should not put all his eggs into one basket. He should diversify his portfolio, i.e. He should invest this funds in a spread of low and high risk securities in such a way that the total expected return for all his investments is maximized and at the same time the investment risk is minimized. So the research of invest risk becomes of a very important problem which is faced in financial field.The work of Markowitz in portfolio selection has been most influential for the development of modern mathematical finance and its applications in practice, where he applied variance to measure invest risk and constructed the mean-variance model. The common indexes for measuring security investment risk variance of investment return andβ. As the research on risk measure deepens on, it has been found that there are some very severe flaws which can not be avoided when using these indexes.In order to overcome these shortcomings, a lot of research work has been done in theoretical fields. But up to the present, these problems have not been solved satisfactorily. This thesis does study these problems mentioned above exactly solved under this circumstance.On the base of Markowitz investment portfolio model and Sharp single-factor model, this paper combines entropy principle with measure of risk on the investment decision making in securities market. On this basis, a new portfolio models using entropy to measure risk are proposed.Finally, using the Matlab software, we analyses the investment decision of 20 index stocks of Shenzhen Security Market. Suitable stocks selecting by this model have been made optimal portfolios model. Furthermore, the efficient frontier derived by the optimal portfolios of stocks selecting by Single-Factor model of investment portfolio based on entropy can fit efficient frontier optimal portfolios derived from the whole stocks.