Optimal reinsurance design under distortion risk measures and reinsurer's default risk with partial recovery

Yong, Yaodi1; Cheung, Ka Chun2; Zhang, Yiying1

2024-10-01

10.1017/asb.2024.24

ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION   影响因子和分区

0515-0361

1783-1350

Reinsurers may default when they have to pay large claims to insurers but are unable to fulfill their obligations due to various reasons such as catastrophic events, underwriting losses, inadequate capitalization, or financial mismanagement. This paper studies the problem of optimal reinsurance design from the perspectives of both the insurer and reinsurer when the insurer faces the potential default risk of the reinsurer. If the insurer aims to minimize the convex distortion risk measure of his retained loss, we prove the optimality of a stop-loss treaty when the promised ceded loss function is charged by the expected value premium principle and the reinsurer offers partial recovery in the event of default. For any fixed premium loading set by the reinsurer, we then derive the explicit expressions of optimal deductible levels for three special distortion functions, including the TVaR, Gini, and PH transform distortion functions. Under these three explicit distortion risk measures adopted by the insurer, we seek the optimal safety loading for the reinsurer by maximizing her net profit where the reserve capital is determined by the TVaR measure and the cost is governed by the expectation. This procedure ultimately leads to the Bowley solution between the insurer and the reinsurer. We provide several numerical examples to illustrate the theoretical findings. Sensitivity analyses demonstrate how different settings of default probability, recovery rate, and safety loading affect the optimal deductible values. Simulation studies are also implemented to analyze the effects induced by the default probability and recovery rate on the Bowley solution.

Optimal reinsurance default risk partial recovery expected value premium principle Bowley solution C61 G22 G32

SCI ; SSCI

英语

第一 ; 通讯

Research Grants Council of the Hong Kong Special Administrative Region, China[17303721] ; National Natural Science Foundation of China["12101336","72311530687"] ; Guangdong Basic and Applied Basic Research Foundation[2023A1515011806] ; Shenzhen Science and Technology Program[JCYJ20230807093312026]

Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences

Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods ; Statistics & Probability

WOS:001325622100001

CAMBRIDGE UNIV PRESS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
2.Univ Hong Kong, Dept Stat & Actuarial Sci, Pokfulam Rd, Hong Kong, Peoples R China

Yong, Yaodi,Cheung, Ka Chun,Zhang, Yiying. Optimal reinsurance design under distortion risk measures and reinsurer's default risk with partial recovery[J]. ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION,2024.

Yong, Yaodi,Cheung, Ka Chun,&Zhang, Yiying.(2024).Optimal reinsurance design under distortion risk measures and reinsurer's default risk with partial recovery.ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION.

Yong, Yaodi,et al."Optimal reinsurance design under distortion risk measures and reinsurer's default risk with partial recovery".ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION (2024).