The Application Of Multiple Q-gaussian Distribution In Portfolio Model

Multiple q-gaussian distribution is a kind of generalized gaussian distribution,it well describes some complex system characteristics and is widely used in various fields of science, for example,the social, economic and natural science, life science and so on. its density function is deduced by stochastic differential equation with white noise,and theoretical research for multiple q-gaussian distribution is very less, so we study multiple q-gaussian distribution for theorety. it found that the distribution similar to gaussian distribution in a certain parameters range but has tip peak and thick tail nature.Portfolio theory is in a certain income level down investment risk minimization or in a certain risk level down the income maximization. Traditional portfolio model assumes that the rate of return accord with gaussian distribution, but this often doesn’t accord with the actual financial markets.The actual financial market rate of return has tip peak and thick tail characteristics, it just conforms to that multiple q-gaussian distribution has properties with tip peak and thick tail.Therefore it needs the investment portfolio model which based on gaussian distribution for correction, and establishs a new investment portfolio model that is based on multivariate q-gaussian distribution.This paper contains the following aspects of the work:1. Discuss the theory of multivariate q-gaussian distribution, detailedly derived process from stochastic differential equation with white noise to multiple q-gaussian density function,we prove that the parameter q take a certain range it is a density function, the paper discusses the approximate density function expression; discussed the binary q-gaussian distribution graphics, and compared with gaussian distribution, with peak thick tail sex, discuss when parameter change graphic change;discussed the multiple q-gaussian distribution statistical properties; Finally discussed the multiple q-gaussian distribution’s digital features (such as mean vector, covariance matrix) and the estimation of parameter of multiple q-gaussian distribution2.Due to multiple q-gaussian distribution has peak thick tail characteristics, conform to the current financial market actual characteristics.we fixed the classic the investment portfolio model and build mean-variance portfolio model and mean-VAR portfolio model based on multivariate q-gaussian distribution and the solve for these models.3.This paper selects chinese three stocks(sz00062,000025,000037)in A-share market,we statistically analysis rate of return from January2011to March2012, find that three stock return don’t meet the gaussian distribution, but satistical distribution has more tip peak and thick tail than gaussian distribution,gaussian distribution fits better, calculate the covariance matrix for multiple q-gaussian distribution, then find out optimal investment proportion based on multivariate q-gaussian distribution and multivariate gaussian distribution.we simulated invest the three stock in April2012by calculated proportion,calculations show that of these mean-VAR portfolio model which based on multivariate q-gaussian distribution for three stocks is the better than others,Based on multivariate q-gaussian distribution the two investment portfolio model is better than other two based on gaussian distribution model.