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Bivariate maximum insurance claim and related point processes

Listed author(s):
  • Hashorva, Enkelejd
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    Let 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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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 2 (August)
    Pages: 117-128

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:2:p:117-128
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    1. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.
    2. Li, Y. & Pakes, Anthony G., 2001. "On the number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 309-323, June.
    3. Hashorva, Enkelejd & Hüsler, Jürg, 2001. "On the number of points near the multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 113-124, November.
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