Portfolio Optimization And Its Dynamic Analysis

Theory of portfolio optimization is an important part of the modern ?nance in-vestment theories, Which uses mathematical facilities such as convex analysis, randomanalysis, nonsmooth analysis, (nonlinear) programming etc, combined with the mean-variance method－the basic method of modern portfolio theory. By setting up mathe-matical models, discussed the investment rules of ?nance market and o?ered theoreticguide for investors. The main results of the thesis can be summarized as follows: ? Several basic portfolio models have been summarized ?rstly; ? Considering the real market conditions, a minimax model with transaction costs as well as no short sales is developed for optimal portfolio selection and the dynamic rules with transaction costs rate changing is analyzed secondly; ? The structure of M-V portfolio e?cient frontier and its changes are studied if short sales are not allowed, by adjusting the original securities set such that the M-V e?cient frontier of new securities set get better; ? Sensitivity analysis to the e?cient frontier and the optimal solution of the portfolio with lower budge constraint are studied when mean or risk of some security is changeable; ? The portfolio selection models with the ?xed consumption-income and the continuous-time incomplete information are introduced ?nally.