Principles that uniquely determine simple risk-sharing rules

Risk-sharing arrangements—where a group agrees to split losses from uncertain events—are increasingly discussed in decentralized and community-based settings. However, groups often start by agreeing on principles; for example, protecting participants' information, avoiding punitive allocation processes, and aiming for equitable sharing, rather than on a specific mathematical rule. This raises an important question: which risk-sharing rule is implied by a chosen set of principles—and what principles are implicitly endorsed by choosing a given rule?

In a paper published in Risk Sciences, Jan Dhaene, Rodrigue Kazzi, and Emiliano A. Valdez present an axiomatic approach to this question. They formalized properties that a rule may satisfy, such as reshuffling (swapping participants' losses swaps their contributions in the same way), source-anonymous contributions (contributions do not depend on which participant experienced which loss), and aggregate contributions (contributions depend only on the total loss, not on the individual breakdown).

Using these concepts, the team showed how familiar rules can be understood as the unique outcomes of particular combinations of axioms. For instance, they established that equal sharing (the uniform rule) is singled out by combining reshuffling with source-anonymous contributions.

As the authors write: "To illustrate, we demonstrate that the uniform RS rule, a simple mechanism in which risks are shared equally, is the only RS rule that satisfies both the reshuffling and source-anonymous contributions properties." They then extend the same logic to characterize broader families of rules, including proportional and linear forms that incorporate more information about participants' risks.

The framework also accommodated scenario-based approaches that rely on agreed-upon "typical" (and, in some cases, extreme) scenarios, offering a practical option when probability-based modeling is not feasible.

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Contact the author:

Rodrigue Kazzi (corresponding author)

Actuarial Research Group, KU Leuven, Belgium

rodrigue.kazzi@kuleuven.be

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