Abstract
We consider a risk model with three types of claims: ordinary, leading, and descendant claims. We derive an expression for the Laplace–Stieltjes transform of the distribution of the discounted aggregate claims. By using this expression, we can then obtain the mean and variance of the discounted aggregate claims. For actuarial applications, the VaR and CTE are computed by numerical inversion of the Laplace transforms for the tail probability and the conditional tail expectation of the discounted aggregate claims. The net premium for stop-loss reinsurance contract is also computed.
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Acknowledgements
We are grateful to the reviewers for valuable comments and suggestions, which greatly improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542).
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Yoo, H., Kim, B., Kim, J. et al. Transform approach for discounted aggregate claims in a risk model with descendant claims. Ann Oper Res 293, 175–192 (2020). https://doi.org/10.1007/s10479-019-03392-y
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DOI: https://doi.org/10.1007/s10479-019-03392-y