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Uniform Asymptotics for Finite-time Ruin Probability in a Dependent Risk Model with General Stochastic Investment Return Process

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Abstract

In this paper, we consider a non-standard renewal risk model with dependent claim sizes, where an insurance company is allowed to invest his/her wealth in financial assets, leading to some stochastic investment log-returns described as a general adapted càdlàg process. Under the assumptions that the claim sizes are heavy-tailed and the stochastic log-return process on investments is bounded from below almost surely, we derive some asymptotic formulas for the finite-time ruin probability holding uniformly in any finite time horizon.

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Acknowledgments

The authors are most grateful to the two referees for their very thorough reading of the paper and valuable suggestions. This work was finished during a research visit of Yang Yang to The University of Hong Kong. He would like to thank the Department of Statistics and Actuarial Science for its excellent hospitality.

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Authors and Affiliations

  1. School of Statistics and Data Science, Nanjing Audit University, Nanjing, 211815, China

    Yang Yang & Jun-feng Liu

  2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    Kam Chuen Yuen

Authors
  1. Yang Yang
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  2. Kam Chuen Yuen
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  3. Jun-feng Liu
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Corresponding author

Correspondence to Yang Yang.

Additional information

This paper is supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 20YJA910006), Natural Science Foundation of Jiangsu Province (No. BK20201396), Natural Science Foundation of the Jiangsu Higher Education Institutions (No. 19KJA180003), the Grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU17329216), and the CAE 2013 Research Grant from the Society of Actuaries.

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Yang, Y., Yuen, K.C. & Liu, Jf. Uniform Asymptotics for Finite-time Ruin Probability in a Dependent Risk Model with General Stochastic Investment Return Process. Acta Math. Appl. Sin. Engl. Ser. 37, 847–857 (2021). https://doi.org/10.1007/s10255-021-1050-8

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  • DOI: https://doi.org/10.1007/s10255-021-1050-8

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