On the decomposition of an insurer's profits and losses

TL;DR

This paper develops an axiomatic framework for decomposing insurer profits and losses, revealing that infinitesimal sequential updating is theoretically justified, unlike the commonly used sequential updating method.

Contribution

It introduces an axiomatic approach that explains why infinitesimal sequential updating is the appropriate method for profit and loss decomposition.

Findings

Infinitesimal sequential updating (ISU) decompositions are theoretically justified by axioms.

Current practice often uses sequential updating (SU) instead of ISU.

The axiomatic framework applies broadly beyond insurance contexts.

Abstract

Current reporting standards for insurers require a decomposition of observed profits and losses in such a way that changes in the insurer's balance sheet can be attributed to specified risk factors. Generating such a decomposition is a nontrivial task because balance sheets generally depend on the risk factors in a non-linear way. This paper starts from an axiomatic perspective on profit and loss decompositions and finds that the axioms necessarily lead to infinitesimal sequential updating (ISU) decompositions, provided that the latter exist and are stable, whereas the current practice is rather to use sequential updating (SU) decompositions. The generality of the axiomatic approach makes the results useful also beyond insurance applications wherever profits and losses shall be additively decomposed in a risk-oriented manner.