Merging of bivariate compound binomial processes with shocks

The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some the claim sizes. It is shown that this can be considered as particular case classical compound model. As far we work parallel counting processes in infinite time, if consider them independent, probability event they to have at least once simultaneous jumps would equal one. We overcome problem by using thinning instead convolution operation. bivariate are expressed two ways. characteristics total amount derived. reserve process probabilities ruin discussed. deficit thoroughly investigated when initial capital zero. Its mean, mass function generating obtained. show although global maxima random walk uniquely determined via its vice versa, any geometric distribution non-negative summands has uncountably many stochastically equivalent presentations. survive much more general settings, than those, discussed here, for example Anderson model, Beekman's series