Optimality of general reinsurance contracts under CTE risk measure

Tan, Ken Seng; Weng, Chengguo; Zhang, Yi

doi:10.1016/j.insmatheco.2011.03.002

Cited by 66 publications

(27 citation statements)

References 32 publications

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“…The application of these alternative measures has gained interest growing in literature and industry. In particular, the CT E, due to its properties and its effectiveness in different fields such as finance and actuaries, its use and studies keep increasing (see, e.g., [15], [34], [18], [16] and references therein). In the literature, the estimation of the CT E and its asymptotic normality under the assumption that the second moment of the loss variable is finite has been established but this assumption is very restrictive in practical problems.…”

Section: Introductionmentioning

confidence: 99%

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

Mohamed¹,

Rassoul²,

Rouis³

2020

Stat., optim. inf. comput.

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In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation (CT E) for a loss distribution with a finite mean but infinite variance. The present work introduces a new estimator of the CT E based on the bias-reduced estimators of high quantile for heavy-tailed distributions. The asymptotic normality of the proposed estimator is established and checked, in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the known old estimator.

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Section: Introductionmentioning

confidence: 99%

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

Mohamed¹,

Rassoul²,

Rouis³

2020

Stat., optim. inf. comput.

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“…Another direction that drew substantial attention was the consideration of the optimal insurance contract that minimizes some risk functional, with the most common ones being the value-at-risk (V@R) and the average value-at-risk (AV@R). The problem was studied in Bernard and Tian (2009), Tan et al (2011), Chi and Tan (2011), Chi and Tan (2013), Assa (2015) and Lo (2017a) under different choices of premium principle calculations.…”

Section: Introductionmentioning

confidence: 99%

Optimal XL-insurance under Wasserstein-type ambiguity

Birghila

Pflug

2019

Insurance: Mathematics and Economics

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We study the problem of optimal insurance contract design for risk management under a budget constraint. The contract holder takes into consideration that the loss distribution is not entirely known and therefore faces an ambiguity problem. For a given set of models, we formulate a minimax optimization problem of finding an optimal insurance contract that minimizes the distortion risk functional of the retained loss with premium limitation. We demonstrate that under the average value-at-risk measure, the entrance-excess of loss contracts are optimal under ambiguity, and we solve the distributionally robust optimal contract-design problem. It is assumed that the insurance premium is calculated according to a given baseline loss distribution and that the ambiguity set of possible distributions forms a neighborhood of the baseline distribution. To this end, we introduce a contorted Wasserstein distance. This distance is finer in the tails of the distributions compared to the usual Wasserstein distance.

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“…Cheung (2010) studied the optimal reinsurance with the help of a geometric approach, and generalizes the results in Cai et al (2008). To overcome the lack of generality in that the optimality of the reinsurance designs is confined to reinsurance treaties of specific structure in Cai et al (2008) and Tan and Weng (2010), Tan et al (2011) derived the optimal solutions over all possible reinsurance treaties under the criterion of minimizing CTE of the insurer's resulting risk by resorting to the Lagrangian approach based on the concept of directional derivative.…”

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance Under VaR and CTE Risk Measures When Ceded Loss Function is Concave

Zhi-yi

Liu

Qing-jie

et al. 2014

Communications in Statistics - Theory and Methods

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Cai et al. (2008) explored the optimal reinsurance designs among the class of increasing convex reinsurance treaties under VaR and CTE risk measures. However, reinsurance contracts always involve a limit on the ceded loss function in practice, and thus it may not be enough to confine the analysis to the class of convex functions only. The object of this article is to present an optimal reinsurance policy under VaR and CTE optimization criteria when the ceded loss function is in a class of increasing concave functions and the reinsurance premium is determined by the expected value principle. The outcomes reveal that the optimal form and amount of reinsurance depend on the confidence level p for the risk measure and the safety loading θ for the reinsurance premium. It is shown that under the VaR optimization criterion, the quota-share reinsurance with a policy limit is optima, while the full reinsurance with a policy limit is optima under CTE optimization criterion. Some illustrative examples are provided.

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Optimality of general reinsurance contracts under CTE risk measure

Cited by 66 publications

References 32 publications

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

Optimal XL-insurance under Wasserstein-type ambiguity

Optimal Reinsurance Under VaR and CTE Risk Measures When Ceded Loss Function is Concave

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