Abstract
In the presence of reinsurance, an insurer may effectively reduce its (aggregated) loss by partially ceding such a loss to a reinsurer. Stop-loss and quota-share reinsurance contracts are commonly agreed between these two parties. In this paper, we aim to explore a combination of these contracts. The survival functions of the ceded loss and the retained loss are firstly investigated. Optimizing such a reinsurance design is then carried out from the joint perspective of the insurer and the reinsurer. Specifically, we explicitly derive optimal retentions under a criterion of minimizing a convex combination of conditional tail expectations of the insurer’s total loss and the reinsurer’s total loss. In addition, an estimation procedure and more explanations on numerical examples are also presented to find their estimated values.
Highlights
Under a reinsurance contract, a loss faced by an insurer is partially ceded to a reinsurer.As a consequence, the insurer is liable for the remaining loss, called the retained loss, and a fixed reinsurance premium, which has to be paid to the reinsurer
The goodness of the Pareto distribution in fitting the empirical distribution of the data may be observed in According to the estimated Pareto distribution for the claim data, we compute the estimates for the optimal retention limit and the objective function denoting the convex combination of the conditional tail expectation (CTE) when the combined stop-loss and quota-share reinsurance is agreed between an insurer and a reinsurer
For various values of these retentions, the survival functions of the loss retained by the insurer and the loss covered by the reinsurer are investigated
Summary
A loss faced by an insurer is partially ceded to a reinsurer. Under these two risk measures, the optimal reinsurance can be in the form of stop-loss, quota-share, or their combination The optimization on the former two reinsurance contacts was investigated further by Tan et al (2009) who employed the VaR- and CTE-based criteria. The above optimization criterion was adopted by Jiang et al (2017), Fang et al (2019), and Chen and Hu (2020) by using the same VaR risk measure They found that the combined stop-loss and quota-share reinsurance is one of the optimal solutions to their optimization problems.
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