Multi-factor Portfolio Model And Its Evolutionary Programming Algorithm Research

The portfolios theory is one of the important research contents in the field of mathematical finance. It aims to attain the optimal portfolios by maximizing investment's return or minimizing investment's risk under the condition of uncertain factors affect. The Multifactor Pricing Model is a more complex model, which has the character of Markowitz's model and can explain invest-activity more clearly.(1) We introduce Markowitz's model, discuss the result of single factor model, and make a discourse of Multifactor portfolio model.(2) Based on the former research work, we make an improvement of the portfolio theory. Under the condition of holding risk-free security, we simplify Markowitz's model for portfolio investment and establish the optimal model under the condition of short sale allowed and no short sale. We study the existence of the model's result and the exclusive of that, work out the expression of the model's result, analyze thecharacter of vector B, for example, how it effects the rate of return or the risk ofportfolio. At last, we study the relationship between the results of the two models under the condition of short sale allowed or unallowed.(3) We solve the model of portfolio by using Evolutionary Programming under the condition of the covariance matrix which is a non-positive matrix, design the methods which can solve Markowitz's model and Multifactor portfolio model. And we improve on Markowitz's model, establish the optimal model under the conditions that the investor is risk-avoid or risk-like.(4) Finally, we introduce other risk concepts, propose some new questions which need further research under different measure of risk.