A General Surplus Decomposition Principle in Life Insurance

TL;DR

This paper introduces a universal surplus decomposition principle for life insurance, enabling fair allocation of surplus to policies and risk sources through an innovative, mathematically grounded approach.

Contribution

It presents the ISU decomposition principle, a novel, overarching method for surplus decomposition based on infinitesimal sequential valuation updates, unifying existing heuristics.

Findings

Existing heuristic decompositions can be replicated as ISU decompositions.

The ISU principle offers a general framework applicable beyond classical life insurance surplus analysis.

Alternative decomposition methods are related to the ISU approach.

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.