Applied Research On Economic Life In Optimization Theory

Optimization Theory is the most important subject in application areas, it studies the best method of the decision-making problem.The Portfolio Investment Model and the Principal-Agent Theory are the most important part.Based on Optimization Theory, this thesis studies these models.The main content and achievement of this thesis are:Based on the model of Markowitz's Portfolio Investment:in chapter 1, the thesis studies the model when the covariance matrices are general symmetric matrices, gets an extension on an important theorem, discusses the solution of the model following two classes of the general symmetric matrices, and gives a method for calculating optimal portfolio.Based on the decision tree method of the portfolid investment ,in chapter 2, the thesis proposes the improved decision tree method, and discusses how to use this method to select and rank the alternatives of the portfolio investment.In chapter 3, the conception and the categories of Principal-Agent problem, the framework of the Principal-Agent Theory, the reasons and the behavior of the Principal-Agent problem in Privately Offered Fund are introduced. It is mentioned that the decision for the investor is how to allocate his capital in asymmetric information.In chapter 4,to solve the asymmetric information decision-making problem of the Privately Offered Fund investor, the thesis sets up a model and makes the analysis. The results show that the audit cost affects the decision greatly and the investment situations change better with lower audit cost or change worse with high audit cost.