Non-linear Complexity Of Capital Market And Portfolio Optimization

In classical Capital Market Theory (CMT), Efficient Market Hypothesis (EMH) is the headstone of CMT at all times. But some researches have testified that the classical CMT can't interpret a lot of practices. It is causation that the classical CMT research capital market based on a linear mode. While the realistic capital market always react exoteric action with a nonlinear mode. In this paper, we will discuss both the nonlinear complexity of CMT and the intelligent optimization of portfolio by integrating nonlinear technology and intelligent optimization method with CMT, which can not only enrich CMT and boost the development of CMT but also can promote the establish of Computable Finance which is effective. On this background, we start our research from the non-linearity of CMT and empirical study both nonlinear character and chaos character of china stock market. On the basis of it, we also research both portfolio selection model and portfolio management with intelligent optimization method, which may makes bath investment behavior and investment management of investor to accord with reality of capital market.We firstly empirical study non-linear characters of both shanghai stock market and shenzhen stock market by using month, week and day's return data applying Hurst index and R/S analysis method. We obtain their Hurst exponent,correlation coefficient,fractal dimension and non-periodic cycle by means of analysing data from high frequency to low frequency. Further, we analysis different frequency data in the inner of both shanghai stock market or shenzhen stock market with comparative method, and obtain their exact non-linear characters. We also comparatively analysis the non-linear characters of both shanghai stock market and shenzhen stock market in their exterior, and obtain that the non-linear characters of shanghai stock market is different with shenzhen stock market's. The empirical results indicate that both shanghai stock market and shenzhen stock market all exist state persistence, and that the fluctuation of china stock market present correlation dependent, and the time series that china stock price index form take on non-linearity character, and their return don't submit to normal distribution. These illuminate that china stock market isn't efficient market, but is non-linear capital market. Subsequent, we also reconfigure the phase space of both shanghai stock market and shenzhen stock market by using reconfiguration phase space technology, and picture their 2-dimension and 3-dimension trend charts. Then we respectively calculate the correlation dimension of both shanghai stock market and shenzhen stock market, and find their saturated embed dimension that illuminate shanghai and shenzhen stock market are low-freedom chaos systems which have a fractional dimension structure. Further, we respectively calculate the Lyapunov exponent of both shanghai stock market and shenzhen stock market, and find their values all greater than zero, which illuminates both shanghai stock market and shenzhen stock market are chaos systems, which furtherly interprets mechanics of forming non-linear complexities of capital market. At last, we also comparatively analysis chaos character of shanghai stock market and shenzhen stock market, obtain that shanghai stock market exists more powerful chaos phenomenon.On the basis of the non-linear complexities of capital market, we discuss existence and importance of the return skewness, and induct skewness into mean-variance model. Hence, we educe mean-variance-skewness model, compare their effective front edge with empirical study method. Further, we analyse the effects of expected skewness level to mean-variance-skewness model. Otherside, we have established mean-variance-skewness model based on the fuzzy market by introducing some market friction factors into mean-variance-skewness model, and analyse the effects of some market friction factors to investment results of mean-variance-skewness model. We also establish bi-object portfolio model based on the friction m...