The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

Abstract

In this study, we take the conditional tail expectation (CTE) as the constraint condition and consider the optimal reinsurance issues under Wang’s premium principle in general insurance contracts. With the confidence level and the distortion function in Wang’s premium principle given by the insurer in advance, a threshold can be obtained. When the insurer’s risk tolerance level is greater than this value, the optimal reinsurance is a proportional reinsurance in which the deductible equals to this value, else the optimal form of reinsurance is a stop-loss reinsurance. Corresponding numerical examples and economic explanations are also given.

Designing of Optimal Reinsurance Indemnity

“…VaR and TVaR as criteria were applied by Zhang et al [17] and Zhang et al [6] concerning winning mutual benefits for both sides, insurer and reinsurer. CTE, as a condition in combination with Wang's premium principle, was analysed by Hu et al [7]. To outline, it could be noticed that risk measures such as VaR, CTE and TVaR are used and analysed frequently under miscellaneous conditions.…”

“…For instance, Zhang et al [6] used VaR and tail value at risk (TVaR). In addition, Hu et al [7] used CTE in their study.…”

The Combined Stop-Loss and Quota-Share Reinsurance: Conditional Tail Expectation-Based Optimization from the Joint Perspective of Insurer and Reinsurer

“…Meanwhile, Zhou et al (2011) and Putri et al (2021) investigated the optimality of the combination of quota-share and stop-loss reinsurance. The other studies on the reinsurance optimization from the insurer's viewpoint under the above risk measures may be found in Lu et al (2014), Lu et al (2016), Du et al (2019), and Hu et al (2021). In contrast, optimizing the reinsurance treaty from the perspective of a reinsurer was undertaken by Tan et al (2020).…”