In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with cádlág paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.
Poisson risk model tail probability one-sided linear process heavy-tailed distribution asymptotic upper bound investment return
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Guo’s work was supported by National Natural Science Foundation of China (Grant No. 71501100) and the Open Project of Jiangsu Key Laboratory of Financial Engineering (Grant No. NSK2015-02). Wang’s work was supported by National Natural Science Foundation of China (Grant No. 71271042). This article is one of the stage results of the Major Bidding Project of the Chinese National Social Science Foundation (Grant No. 17ZDA072).
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