Conditional Tail Expectation and Premium Calculation under Asymmetric Loss

In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an...

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Bibliographic Details
Published in:Axioms 2023-05, Vol.12 (5), p.496
Main Authors: Calderín-Ojeda, Enrique, Gómez-Déniz, Emilio, Vázquez-Polo, Francisco J.
Format: Article
Language:English
Subjects:
asymmetric loss function
Asymmetry
composite models
Functional equations
Functions
Insurance premiums
loss distributions
Methods
Policyholders
premium calculation
Random variables
Risk
Risk assessment
risk measures
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Summary:In this paper, we calculate premiums that are based on the Conditional Tail Expectation (CTE) and asymmetric loss functions to account for the risk of both underestimation and overestimation losses. After selecting an appropriate loss function, the premium is calculated as the quantity minimizing an objective function related to the conditional tail expectation of the loss. The premium satisfies desirable properties, i.e., it is a coherent risk measure, and it helps the practitioner to quantify the global risk of the insurer. Finally, this methodology is applied to quantify the risks associated to the total claims amount that are modelled via composite models and comparisons with the usual risk measures, i.e., Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are carried out.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12050496