Analysis of Bivariate Excess Losses

By Jiandong Ren

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The concept of excess losses is widely used in reinsurance and retrospective insurance rating. The mathematics related to it has been studied extensively in the property and casualty actuarial literature. However, it seems that the formulas for higher moments of the excess losses are not readily available. Therefore, in the first part of this paper, we introduce a formula for calculating the higher moments, based on which it is shown that they can be obtained directly from the Table of Insurance Charges (Table M). In the second part of the paper, we introduce the concept of bivariate excess losses. It is shown that the joint moments of bivariate excess losses can be computed through methods similar to the ones used in the univariate case. In addition, we provide examples to illustrate possible applications of bivariate excess loss functions.

Keywords: Reinsurance, Bivariate Excess Loss, Table M


Ren, Jiandong, "Analysis of Bivariate Excess Losses," Variance 10:2, 2018, pp. 195-203.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.