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Large deviations for the stochastic present value of aggregate net claims with infinite variance in the renewal risk model and its application in risk management

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Abstract

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric present Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of aggregate claims. In this paper, the large deviation for the stochastic present value of aggregate net claims, when the net claim size distribution is of Pareto type with finite expectation are obtained. We conduct some simulations to check the accuracy of the result we obtained and consider a portfolio optimization problem that maximizes the expected terminal wealth of the insurer subject to a solvency constraint.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 71671166) and the Talent start-up fund of China Three Georges University (Grant No. 1910103).

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Authors and Affiliations

  1. School of Statistic and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Min Xiao, Ruixing Ming & Tao Jiang

  2. College of Science, China Three Gorges University, Yichang, 443002, China

    Sheng Cui

Authors
  1. Min Xiao
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  2. Sheng Cui
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  3. Ruixing Ming
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  4. Tao Jiang
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Correspondence to Tao Jiang.

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Xiao, M., Cui, S., Ming, R. et al. Large deviations for the stochastic present value of aggregate net claims with infinite variance in the renewal risk model and its application in risk management. Cluster Comput 21, 997–1007 (2018). https://doi.org/10.1007/s10586-017-1007-0

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  • DOI: https://doi.org/10.1007/s10586-017-1007-0

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