The Minimal Symmetric ? Entropy Martingale Measure And The Valuation Problem Incomplete Market

Under the assumption that the set Me?(?)of equivalent martingale measures,the article first gives the definition of the minimal symmetric ? entropy martingale mea-sure and the intuitional interpretation of the minimal symmetric ? entropy martingale measure,Secondly,we give the sufficient condition for the existence of the minimum symmetric ? entropy martingale measure and give the density representation(Radon-Nikodym derivative)of the minimum symmetric ? entropy martingale measure.Again,in the specific financial environment,the relationship between the minimization symmet-ric ? entropy and the maximization of the utility function is described by comparing the equation satisfying the utility function of the minimum symmetric ? entropy martingale measure and the equations corresponding to the two common utility functions.Finally,the minimum symmetric ? entropy martingale measure is closer to the real financial market by comparing the minimum symmetric ? entropy martingale and the minimum symmetric entropy martingale measure.