Statistics and Its Interface

Volume 8 (2015)

Number 1

Special Issue on Extreme Theory and Application (Part II)

Guest Editors: Yazhen Wang and Zhengjun Zhang

Uniform asymptotics for ruin probabilities in a nonstandard compound renewal risk model

Pages: 3 – 8

DOI: http://dx.doi.org/10.4310/SII.2015.v8.n1.a1

Authors

Yang Yang (School of Mathematics and Statistics, Nanjing Audit University, Nanjing, China; and School of Economics and Management, Southeast University, Nanjing, China)

Zhongquan Tan (College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, China)

Yunyun Zhong (School of Mathematics and Statistics, Nanjing Audit University, Nanjing, China)

Abstract

In this paper, we consider a nonstandard compound renewal risk model with or without a constant interest rate, in which claims at each accident moment are aggregated from a number of widely orthant dependent individual claims, and inter-arrival times are widely lower orthant dependent. We establish some asymptotic formulae for the finite-time and infinite-time ruin probabilities, when the individual claims are heavy-tailed. The obtained asymptotics hold uniformly on a finite or infinite time interval.

Keywords

compound renewal risk model, uniform asymptotics, finite-time and infinite-time ruin probabilities, heavy tail, dependence

2010 Mathematics Subject Classification

Primary 62E10, 62P05. Secondary 60F05.

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