We consider decentralized risk-sharing pools, where each participant is compensated from the pool for his loss and in return he pays an ex-post contribution to the pool. The contributions of the participants follow from an appropriate risk-sharing rule, which is chosen such that the sum of all individual contributions to the pool is equal to the aggregate loss of the pool. We introduce and discuss a list of relevant properties of risk-sharing rules. A number of candidate risk-sharing rules are considered, including the conditional mean risk-sharing rule and the quantile risk-sharing rule. Their compliance with the proposed properties is established.

Jan Dhaene is a full professor in actuarial science with the Research Centre Insurance, Department of Accountancy, Finance and Insurance at the Faculty of Economics and Business, KU Leuven. His main current research interests are in modeling dependencies in insurance portfolios, incorporating stochastic financial aspects in actuarial models, risk management for financial institutions and integrating financial and actuarial models. He has published over 135 scientific papers in refereed journals. Together with R. Kaas, M. Goovaerts and M. Denuit, he is a co-author of the books “Modern Actuarial Risk Theory”, Kluwer, 2001, “Actuarial Theory for Dependent Risks”, Wiley, 2005 and “Modern Actuarial Risk Theory, using R”, Springer, 2008. He has been co–chair holder of the Fortis Chair in Financial and Actuarial Risk Management (2006-2009) and chairholder of the AG Insurance Chair in Health Insurance (2010-2019). Homepage: https://jandhaene.org/