Uniform asymptotics for the finite-time and infinite-time ruin probabilities in a dependent risk model with constant interest rate and heavy-tailed claims
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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.
Keywordsuniform asymptotics finite-time and infinite-time ruin probabilities dominatedly varying tail long tail dependence
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- 8.Y. Chen, W. Zhang, and J. Liu, Asymptotic tail probability of randomly weighted sum of dependent heavy-tailed random variables, Asia-Pac. J. Risk Insur., 4(2):Article 4, 2010.Google Scholar
- 27.K. Wang, Y. Wang, and Q. Gao, Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate, Methodol. Comput. Appl. Probab., 2011, doi: 10.1007/s11009-011-9226-y.