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

Khreshna Syuhada, Arief Hakim and Suci Sari
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Khreshna Syuhada: Statistics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia
Arief Hakim: Statistics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia
Suci Sari: Statistics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia

Risks, 2021, vol. 9, issue 7, 1-21

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.

Keywords: conditional tail expectation; optimal retention; reinsurance; survival function (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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