A general surplus decomposition principle in life insurance. Issue 10 (26th November 2022)

• Record Type: Journal Article
• Authors: Jetses, Julian; Christiansen, Marcus C.
• Is Part Of: Scandinavian actuarial journal. Volume 2022:Issue 10(2022)
• Page Start: 901
• Page End: 925
• Publication Date: 2022-11-26
• Subjects: With-profit life insurance -- bonus and dividends -- profit and loss attribution -- redistribution of surplus -- sequential decompositions; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2022.2049636
• Languages: English
• ISSNs: 0346-1238

Abstract

ABSTRACT: In with-profit life insurance, the prudent valuation of future insurance liabilities leads to systematic surplus that mainly belongs to the policyholders and is redistributed as bonus. For a fair and lawful redistribution of surplus, the insurer needs to decompose the total portfolio surplus with respect to the contributions of individual policies and with respect to different risk sources. For this task, actuaries have a number of heuristic decomposition formulas, but an overarching decomposition principle is still missing. This paper fills that gap by introducing a so-called ISU decomposition principle that bases on infinitesimal sequential updates of the insurer's valuation basis. It is shown that the existing heuristic decomposition formulas can be replicated as ISU decompositions. Furthermore, alternative decomposition principles and their relation to the ISU decomposition principle are discussed. The generality of the ISU concept makes it a useful tool also beyond classical surplus decompositions in life insurance.