ИСТИНА

In many applications we need to use multivariate risk models which have some specific properties: their components are dependent, every component has the property of long-range-dependence, the correspondent distributions have heavy tails. In our report we consider the examples of such models. To construct such models we use the general variant of so called reduction method and subordinated processes. Next we consider some applications of these models: estimation of ruin probability in multivariate collective risk model, estimation of Tail Conditional Expectation for a portfolio components, upper and lower bounds for buffer overflow probability in teletraffic theory.