Network methods of separation of mixtures of probability distributions and their application to the decomposition of volatility indexes

Methods are proposed for the statistical separation ofmixtures of probability distributions based on theminimization of the discrepancy between the theoretical and empirical distribution functions. Main attention is paid to the minimization of $\sup$- and $L_1$-norms of the discrepancy. It is demonstrated that these problems can be reduced to problems of linear programming. The simplex-method is used for their numerical realization. The proposed methods are applied to the problem of decomposition of the volatility of financial indexes. Examples of the decomposition of the volatility of AMEX, CAC 40, NIKKEI, and NASDAQ indexes are presented.