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Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Jiangsu Key Laboratory of Financial Engineering and School of Finance, Nanjing Audit University, Nanjing, 211815, China

    Fenglong Guo

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Dingcheng Wang

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  1. Fenglong Guo
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  2. Dingcheng Wang
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Correspondence to Dingcheng Wang.

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Guo, F., Wang, D. Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return. Sci. China Math. 62, 735–750 (2019). https://doi.org/10.1007/s11425-017-9167-0

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  • DOI: https://doi.org/10.1007/s11425-017-9167-0

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