Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 934-942.

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Precise Large Deviations for a Bidimensional Risk Model with the Regression Dependent Structure

Zhenlong Chen1(),Yang Liu1(),Ke-ang Fu1,2,*()   

  1. 1 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
    2 Department of Statistics, Zhejiang University City College, Hangzhou 310015
  • Received:2021-03-23 Online:2022-06-26 Published:2022-05-09
  • Contact: Ke-ang Fu;;
  • Supported by:
    the NSFC(11971432);the NSSFC(20BTJ050);the NSF of Zhejiang Province(LY21G010003);the Zhejiang Province Focuses on the Construction of Advantageous and Characteristic Disciplines in Universities(Statistics of Zhejiang Industrial and Commercial University)


In this paper, we consider a non-standard bidimensional risk model, in which the claim sizes $ \{\vec{X}_k=(X_{1k}, X_{2k})^T, $ $k\ge 1\}$ form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other, and there exists a regression dependent structure between these vectors and the inter-arrival times. By assuming that the univariate marginal distributions of claim vectors have consistently varying tails, we obtain the precise large deviation formulas for the bidimensional risk model with the regression dependent structure.

Key words: Bidimensional risk model, Consistently varying tail, Precise large deviations, Regression dependence

CLC Number: 

  • O211.4