Multidimensional probability models with dependent components

The special type of dependency, generated by convolution procedure with "overlapping" components is considered. It is a basis of multivariate collective risk model with dependent components of claim arrival process and dependent claim amount distribution. We investigate some properties of offered model, in particular ruin probability. Also we consider the special form of multivariate dependent Gamma distribution and calculate their tail conditional expectation, multivariate generalization of Panjer recursive procedure for compound Poisson distribution is introduced.