The Application Of Stochastic Dynamical Systems In The Portfolio

Nowadays, society has entered into economic competition time, the development of society and the requirement for human progress induce people to devote more and more energy to finance and economics research. For decades of development, people increasingly look for better theoretical systems to improve finance development and innovation. Some economic problems especially portfolio are studied in this thesis by use of random dynamical system theory.This thesis deals with the following two creative topics :The first part is finished on the base of Klaus' working paper "Evolution of Portfolio Rules in Incomplete Market". Klaus utilize random dynamical system theory to set up a model for market share and invest share. Moreover an explicit formula for the best investment strategy in the future time is derived. The significance this result brought is the investor who selects this strategy will be the only survivor and dominate total market wealth. For this reason, we want to own this result and carry it out on China financial market. However whether this theory adapt to China market is a susceptible problem. Therefore we pay much attention to confirmation study in the first part. The technique we proposed is to take the original stock data on China stock market from year 2000 to 2001 as material, and select final data per day of several representational stocks as fundamental data, then put data into that three important formula. This thesis taking two assets, five assets, ten assets and five investors, ten investors as example, obtains wealth evolution within 150 days. At the same time financial significance involved in the graph is also analyzed in detail. At last we come to the conclusion: Klaus theory in shape with China stock market.The second part focuses on the theoretical task. Being inspirited by [1], invest share and market share in the incomplete market are considered once more. In this sector market wealth is admitted to change and every investor can withdraw a part of his wealth during investment, which are reverse to those hypotheses of Klaus. WeWe place our study within the theory of random dynamical system, as a result we get a new random equation model. With the law of large number and temper property, a fixed point of market share in the future time can be found when total wealth of market is changeable. It is proved that this fixed point is stable. At the end of this thesis, a simple explanation for economic significance of it is provided.