Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models

In this paper, we consider uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional renewal risk models with constant interest forces and diffusion generated by Brownian motions. In one of the models, two classes of claims have different arrival times, whi...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2013-05, Vol.401 (1), p.114-129
Main Authors: Chen, Yang, Wang, Le, Wang, Yuebao
Format: Article
Language:English
Subjects:
Bidimensional risk model
Finite-time ruin probability
Uniform asymptotics
Upper tail asymptotically independent
Widely lower orthant dependence
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Summary:In this paper, we consider uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional renewal risk models with constant interest forces and diffusion generated by Brownian motions. In one of the models, two classes of claims have different arrival times, while in the another model, two classes of claims share the same arrival times. In both models, two classes of claim sizes are both upper tail asymptotically independent and their distributions belong to the intersection of the long-tailed distribution class and the dominatedly-varying-tailed distribution class, and the inter-arrival times follow a widely lower orthant dependence structure. In each model, we obtain three kinds of uniform asymptotics for the finite-time ruin probabilities, respectively.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.11.046