Studies On The Modeling And Algorithm Of Portfolio Optimization

The aim of portfolio selection is to achieve more profit with less risk. But in the process of investment, profit always companies by risk. In common, the higher the profit, the higher risk, and the lower risk, the lower profit. To disperse the risk, many investors combine some securities, the so called portfolio, to get maximum profit. This makes the research on portfolio become one of the most important subjects in financial literature.Because of the history and system, the research on advanced portfolio in our country started rather late. But after more than ten years endeavor, the scholars in our country have made much advancement in the area. Just based on these, studies on the modeling and algorithm of portfolio are done in the paper.There are four chapters in the paper as following:In the first chapter, some basic concepts related to portfolio are introduced, and at the beginning, the development and the limit of the advanced portfolio are introduced. Then basic content of advanced portfolio theory is introduced, and conclusion and analysis of different portfolio theory are made, including Markowitz mean-variance model, Sharpe CAPM, the single index and multi-factor model and Ross APT. At the end, the late development of advanced portfolio selection is introduced.In the chapter 2, theoretical analysis on the min-max model is given, then further study on algorithm is done and further analysis and comparison of the min-max model and mean-variance model is theoretically given.In the chapter 3, following a brief introduction on the multi-object model and mean-variance model, based on the fact that all the investors are profit lovers, a multi-object model on the portfolio is constructed, and the center-path-following algorithm for solving the multi-object model is given.In the chapter 4, the analysis and comparison of the min-max model given in the chapter 2 and the multi-object model given in the chapter 3 are numerically given.The conclusion of the paper is as following: the multi-object model and the min-max model of portfolio have their own merits and demerits, and they reflect two different mentalities of the investors, so the investors can use different models to do portfolio according to their favorites.