Bivariate maximum insurance claim and related point processes
AbstractLet X1,X2,... be independent bivariate claim sizes arising from an insurance portfolio. The number of claims occurring in the time interval [0,t] is denoted by N(t). We investigate in this paper distributional and asymptotic properties of the following point process:with XN(t):N(t), the bivariate maximum insurance claim occurring during [0,t]. We show that are strongly consistent estimators of a certain tail probability of the claim size distribution. Further, we investigate the connection between convergence in distribution of the bivariate maximum claim size and weak convergence of . As a byproduct, a result for the ECOMOR reinsurance treaty is obtained.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 69 (2004)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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