On the decomposition of an insurer's profits and losses

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 non-trivial 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.

KEYWORDS:

• IFRS 17
• solvency II
• change analysis
• surplus decomposition
• conditional risk measure

Acknowledgements

The author wants to thank two anonymous referees whose comments have been very helpful to improve a previous version of the present work.

Disclosure statement

No potential conflict of interest was reported by the author.