Abstract
Reinsurance plays a role of a stabilizer of the insurance industry and can be an effective tool to reduce the risk for the insurer. This paper aims to provide the optimal reinsurance design associated with the stop-loss reinsurance under the criterion of value-at-risk (VaR) risk measure. In this paper, the probability levels in the VaRs used by the both reinsurance parties are assumed to be different and the optimality results of reinsurance are derived by minimizing linear combination of the VaRs of the cedent and the reinsurer. The optimal parameter values of the stop-loss reinsurance policy are formally derived under the expectation premium principle.
Highlights
Reinsurance is an effective risk management tool that enables an insurer to reduce the underwriting risk
In order to balance the relationship between the risk retained and the reinsurance premium, the academics started the research of the optimal reinsurance problem
Chi [10] showed that the layer reinsurance is always optimal under both the VaR and CVaR criteria when the reinsurance premium is calculated by a variance related principle
Summary
Reinsurance is an effective risk management tool that enables an insurer to reduce the underwriting risk. Cai and Tan [5] derived explicitly the optimal retained level of a stop-loss reinsurance minimizing the value-at-risk (VaR) and conditional tail expectation (CTE) of the insurer’s total loss under the expected premium principle. Chi and Tan [9] analyzed the VaR-based and conditional-value-at-risk (CVaR)-based optimal reinsurance models over different classes of ceded loss functions with increasing generality. Cai et al [19] studied paretooptimality of reinsurance arrangements under general model settings and obtained the explicit forms of the pareto-optimal reinsurance contracts under tail-value-atrisk (TVaR) measure and the expected value premium principle.
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