The Research Of The Generalized Stop-loss Order≤slm

As we all know, risk theory as an important theoretical study, has been a hot topic of the actuarial profession. And then, as an important tool in the Risk theory, the ordering of risk has been applied widely. Especially in Insurance and Actuarial, the ordering has had an increasingly important influence in the merits of insurance policy and the calculation of premium. Since the20century, Considerable number of scholars have attracted widly and given the discussions and study in theirselves writings. For example Tomasz Rolski has studied the natures of random control order and stop-loss order more in-depth. Shaun Wang and Jan Dhaene has given the stop-loss order and has studied the relationship between stop-loss order and correlation order. In recent years, with the development of society, there is a growing emphasis on the study of risk portfolio. Therefore, a large extent, we need to expand the concept of ordering for actual, and combine the order and some other important concepts (like comonotonicity, etc.) In risk theory, to look forward to more meaningful research results, and then promote the development of insurance mathematics and finance mathematica.This article studied the related results and applications of the generalized stop-loss order≤sim largely. In the second chapter, We mainly reviewed the certain important results in classical orderings and the related properties with the comono-tonic, as a basis for the following discussion general order. In the third chapter, we expanded the stop-loss order to the generalized stop-loss order≤slm first, and then studied the related properties with the generalized stop-loss order<sim, gave the necessary and sufficient conditions when the new order establish, at last, we rela-tionshiped it with other orders which known. In the fourth chapter, we studied the applications of the generalized stop-loss order in comonotonic largely, and also estab-lished the relationship between the new order and comonotonic. In addition, from the perspective of the premium, we introduced the new premium of the general-ized stop-loss order≤slm. From the starting of the risk sequences’ convergence, we reached the relevant theorem which has some practical significance.