Lithuanian Mathematical Journal

, Volume 52, Issue 1, pp 111–121 | Cite as

Uniform asymptotics for the finite-time and infinite-time ruin probabilities in a dependent risk model with constant interest rate and heavy-tailed claims



We consider a nonstandard risk model with constant interest rate. For the case where the claim sizes follow a common heavy-tailed distribution and fulfill a dependence structure proposed by Geluk and Tang [J. Geluk and Q. Tang, Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22:871–882, 2009] while the interarrival times fulfill the so-called widely lower orthant dependence, we establish a weakly asymptotically equivalent formula for the infinite-time ruin probability. In particular, when the dependence structure for claim sizes is strengthened to the widely upper orthant dependence, this result implies a uniformly asymptotically equivalent formula for the finite-time and infinite-time ruin probabilities.

MSC 62P05 62E10 60F05 


uniform asymptotics finite-time and infinite-time ruin probabilities dominatedly varying tail long tail dependence 


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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNanjing Audit UniversityNanjingPR China
  2. 2.Department of MathematicsSoutheast UniversityNanjingPR China
  3. 3.School of Mathematics and PhysicsSuzhou University of Science and TechnologySuzhouPR China

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