How Much Is Optimal Reinsurance Degraded by Error?. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Wang, Yinzhi; Bølviken, Erik
• Is Part Of: North American actuarial journal. Volume 26:Issue 2(2022)
• Page Start: 283
• Page End: 297
• Publication Date: 2022-04-03
• Subjects: Life insurance -- Research -- North America -- Periodicals; Actuarial science -- North America -- Periodicals; Web sites; Electronic journals; 368.010973
• DOI: 10.1080/10920277.2021.1956974
• Languages: English
• ISSNs: 2325-0453

Abstract

Abstract : Estimation error reduces reinsurance optimality under a fitted model to suboptimality under the true one. A mathematical formulation of this issue of degradation is offered and examined through asymptotics as the sample size n of the historical observations becoming infinite. Assuming economic or distortion pricing of reinsurance it is shown that the rate of degradation is either O ( 1 / n ) or O ( 1 n ) depending on smoothness properties of the risk measure employed. Examples are conditional Value at Risk criteria, which tend to be O ( 1 / n ), and Value at Risk, which is O ( 1 / n ) . A numerical study investigates the issue for smaller n and suggests a need for developing more robust optimal reinsurance techniques that can with stand model errors better.