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AN IMPROVED ESTIMATOR OF DISTORTION RISK PREMIUMS UNDER DEPENDENCE INSURED RISKS WITH HEAVY-TAILED MARGINALS
Keywords:
risk premiums, reinsurance, estimation, heavy-tailed, bias reduction, extreme value, dependence serials.DOI:
https://doi.org/10.17654/0972086323014Abstract
Reinsurance is a risk mitigating tool, constituting an important instrument in the management of risk of an insurance company where dependencies and the heavy-tailed nature should be taken into account. When transferring risk, the cedent seeks a trade-off between profit and safety, which is on the nature of the insured underlying risk and on the reinsurance premium calculation principle. Statistical estimations on reinsurance premiums in the heavy-tailed context have been largely studied in the literature, however, only recently dependencies among risks have been considered. In this paper, we propose an improved estimator of distortion risk premiums for dependence re-insured loses with heavy-tailed marginals. Our proposal is based on the extreme value methodology, which offers satisfactory statistical results for such distributions. Moreover, we establish its asymptotic distribution, and through a simulation study, we illustrate its behavior in terms of the absolute bias and the median squared error. The simulation results clearly show that our estimator works well.
Received: March 14, 2023
Revised: May 23, 2023
Accepted: June 9, 2023
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