Abstract

In this work, we propose two frameworks for forming and analyzing the dynamics of smaller groups (sub-groups) within larger risk-sharing schemes. Focusing on a single-period world, we propose subgrouping based on information available before and after the losses are known (ex-ante and ex-post). Subgroups arise naturally in risk-sharing schemes when some individuals share common characteristics and are ‘unequal’ compared to other individuals. For example, consider sharing of healthcare costs between parents and children, or the sharing of natural disaster expenses between developed and developing nations. First, we develop an ex-ante framework for allocating losses to sub-groups within risk-sharing schemes. We extend the work by Denuit and Robert (2022) and adhere to the Pareto-optimal principles proposed by Denuit, Dhaene, Ghossoub, and Robert (2023). This allows for more flexible and equitable loss allocation based not only on individuals’ risk levels, but also on other factors, such as their financial position. We propose modifications to existing risk-sharing rules for the implementation of these principles. Second, we develop an ex-post framework for allocating losses to sub-groups, leveraging additional information available after the realization of losses. Existing risk sharing rules presented in Denuit, Dhaene, and Robert (2022) put all individuals in the ‘same situation’ following allocation of losses. We propose ex-post allocation of losses which encourages sustainability of the risk sharing scheme. This scheme is based on three principles: providing aid only up to the point where it does not cause self-harm, prioritizing aid for those who have experienced large losses, and exempting those experiencing large losses from the obligation to help others in the pool. We present a mathematical formula, equivalent to these principles, that calculates the contribution to the pool for each individual. Finally, we reformulate the expression of risk-sharing rules, allowing our principles to be applied to any arbitrary risk-sharing rule. (The talk is based on joint work with J. Dhaene, R. Kazzi and D. Linders.)

Speaker

Atibhav Chaudry (KU Leuven)