Sensitivity analysis and tail variability for the Wang’s actuarial index

The ranking of insurance risks with respect to their right tail is a challenging problem. In this paper, we extend the actuarial index introduced by Wang (1998) and propose its sensitivity index based on Leser’s perturbation analysis on a proportional hazards model. We use tail variability measures...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2021-05, Vol.98, p.147-152
Main Authors: Psarrakos, Georgios, Vliora, Polyxeni
Format: Article
Language:English
Subjects:
Conditioning
Cumulative residual entropy
Insurance
Mean excess function
Perturbation methods
Proportional hazards model
Right-tail index
Risk
Sensitivity analysis
Statistical models
Studies
Tail variability measures
Variability
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Summary:The ranking of insurance risks with respect to their right tail is a challenging problem. In this paper, we extend the actuarial index introduced by Wang (1998) and propose its sensitivity index based on Leser’s perturbation analysis on a proportional hazards model. We use tail variability measures by conditioning the risk for values greater than the Value-at-Risk (VaR), and we study in detail how the VaR affects the actuarial and the sensitivity index. We provide characterization results for Pareto and exponential distributions, two cases where the actuarial and its sensitivity index are independent from VaR. We also obtain monotonicity results and bounds for them. The results are illustrated by numerical examples.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2021.03.003