| Abstract [eng] |
The aim of this paper is to construct two-dimensional random variables, having one-dimensional ones, carry out the asymptotical analysis and study the speed of convergence. Two-dimensional distribution is constructed in two ways: when the components of random variables are independent and dependent. As in the last few years Pareto distribution is popular in financial models, it was chosen for the analyses. It was proved, that in both cases of independent and dependent components of the vector, the limit distribution is the same. This means that although the components of the vector are dependent, the maxima are asymptotically independent. Besides, the errors are smaller than the approximate estimate. Although, the approximate estimate in the case of independent components is smaller than in the case of dependent components, the errors are on the contrary: they are smaller when the components are dependent than when the components are independent. |
