Equal compensations under actuarially fair contributions in endowment contingency funds

This paper considers risk-sharing schemes, aiming to demonstrate that it is possible to enforce equal compensations by charging actuarially fair contributions. Specifically, consider a group of individuals exposed to the occurrence of a predefined event with adverse financial consequences such as death, survival or being diagnosed with a critical illness for instance. All members of the group agree to contribute in advance a fixed amount to a pool constituted over a reference period with the understanding that the sum of the contributions is shared in arrear among those participants having experienced the predefined event. This allocation is either uniform among claiming participants, each one receiving an equal share of total contributions, or participants are offered the choice to select a desired protection level. In the latter case, participants are free to subscribe one or several units of protection from the fund, and the total amount collected in advance is shared in arrear, equally among all units held by those participants who experienced the predefined event. Endowment contingency funds aim to provide participants with a cheap and effective protection compared to commercial insurance. The reason is that the proposed system is fully funded so that there is no risk borne by the organizer. The benefits in case the event occurs are therefore random but the volatility of the terminal payouts turns out to be limited when the number of participants gets large enough. Under independence, insurance at fair price is recovered at the limit, within infinitely large pools. As an application, the paper considers mutual aid funds and survivor funds. A comparison with takaful insurance is performed.