Research On The Portfolio Selection Models Under Uncertain Circumstance

Modern portfolio theory(MPT) is one of the most exciting part of the Finance andEconomics. Its fascination derives from its preciseness as well as its practicability. Since the famous American economist-Harry Markowitz's original work in 1952, the theory has been in its blossom, and makes a great progress. The portfolio theory has a great application in the assets management of financial organization, the investment tactics of stockjobber, the coordination of state's investment, the selection of personal fortune and all the situation that we need to balance the income and risk. Along with the modern compute technology and development of financial market, the portfolio theory requires to be constantly updated and adapted to new situations with new technology and methods. So this thesis makes some exploration and research on the requirement.The research object of this thesis is portfolio selection problem. The problem is complex and uncertain because of the selection under uncertain circumstance and vagueness of people's thinking and judgment. The thesis commence from the vagueness of the decision information, then analyzes some portfolio selection models based on stochastic theory and fuzzy possiblistic theory. Through using mean-variance model for reference and using fuzzy-random variable to describe the uncertain income of the risk assets, the thesis presents two fuzzy-random programming portfolio selection models which can balance the historical data and expert individual experiences very well. Furthermore the thesis proposes a genetic algorithm based on fuzzy-random simulation to solve two programming models and prove the feasibility of the algorithm through numerical examples.The thesis can be divided into two parts. The first part contains the former three chapter, the last three chapters belong to the second part. Chapter one introduces the history and developing status of modern portfolio theory, propose the structure and innovation point of the thesis. Chapter two introduces fuzzy-random theory including fuzzy-random variable, fuzzy-random programming, fuzzy-random simulation and genetic algorithm. Chapter three analyze the portfolio models based on stochastic theory and the models based on fuzzy theory. Chapter four establish two portfolio selection models with fuzzy-random income and structure a genetic algorithm based on fiizzy-random simulation. Chapter five give a numerical example to show the feasibility of the algorithm. The last chapter summarizes the whole thesis.