Application Of Statistical Analysis In Finance With Random Interval Payoffs

Much uncertainty existed in the financial market with the lack of data, the missing information and something other subjective reasons because of which the uncertainty cannot be described accurately in the classical random financial market. To accurately describe the uncertainty of financial market, the risk measurement based on random interval was put forward in this paper with regarding the return rate of risky asset as a random interval and also some Profit-Risk models was raised based on random interval. Then the Security Market Line(SML) was extended into random interval and the regression analysis was done on the basis of the above.This paper is divided into two parts. The first part is the statistical analysis of random interval. The definition of random interval based on interval number and random sets was given. The definition of algorithm of random interval in virtue of the algorithm and evaluation methodology of interval number and also the upper and lower probability of random sets was put forward next. Then a new probability measure with random sets in virtue of the upper and lower probability was constructed and the distribution function and quantile of random interval was given. The computing method of the mean, the variance, the covariance and some other numerical characteristics of random interval was got by using the pessimism degrees for the defuzzification. On the basis of all the above, the relationships among numerical characteristics, the quality of the correlation coefficient and distance of random interval was analyzed.The second part is the portfolio model based on random interval. The model of return rate of portfolio based on random interval was put forward with regarding the return rate of risky assets as a random interval and combining with the algorithm of random interval. Three Profit-Risk models with random interval was built based on the portfolio model by Markowitz and further combining with the probability measure raised in chapter two the definition of Va R(Value of Risk) with random interval was given and next a new Va R model based on random interval was built. Then the regression analysis was done with adding portfolio returns. Finally a specific numerical example was given based on the stock market of Shanghai using the method of Genetic Algorithm.Random variable is a special form of random interval and the random interval degrade into a random variable when the upper bound and lower bound equals. The conclusion that the numerical characteristics and the quality of statistical analysis and also the risk measurement and other financial models were consistent when the random interval degraded into a random was proved. In general the random variable and random interval were associated and consistent.