some lower and upper bounds for survival function and stop-loss transformation of smallest and largest claim amounts by using stochastic orders

In this paper, we nd simultaneous lower and upper bounds for the survival function and stop-loss transformation of smallest and largest claim amounts by using stochastic orders. we also obtain some lower bounds for the joint survival function of smallest and largest claim amounts, only based on the smallest claim's probabilities, and smallest and largest claim size distributions. the comparisons of smallest and largest claim amounts when the claim sizes vector has some dependent structures to the corresponding based on the independent claim sizes have been dis- cussed. the results established here complete and extend some results of barmalzan et al. (2017).