The article is devoted to the calculation of the dynamic hedge ratio based on three different types of volatility models, among which S-BEKK GARCH model takes into account cross-sectional dependence. The hedging strategy is built for eight stock-futures pairs on energy market in Russia.

In this article we study one class of irrationalities which may be defined as covergent series with rational coefficients. This class contain a lot of well known constants such as $\ln 2$, $\pi$, e.t.c. We consider the problem of determination parameters of rational coefficients by rational approximation of irrationality.    We deduced the lower and upper bounds and present an algorithm for determination of unknown parameters. Also, we present some results of practical calculations.

For n person games with preference relations some types of optimality solutions are introduced. Elementary properties of their solutions are considered. One sufficient condition for nonempty Ca-core is found.