In this paper, we study the strong stability of ruin probabilities in risk models. The question of stability naturally arises in risk theory since the governing parameters in these models can only be estimated with uncertainty. Moreover, in most cases there are not explicit expressions known for the ruin probabilities. Our objective is to present the applicability of the strong stability method to the bivariate classical risk model with independent claims. After clarifying the conditions to

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... oximate the twodimensional risk model with disturbance parameters by the two-dimensional classical risk model, we obtain the stability inequalities with an exact computation of the constants.