Optimal cashback in a cooperative framework for peer-to-peer insurance coverages

The challenges of using technology in the insurance field are opening new horizons for developing and distributing innovative products. Among these, peer-to-peer insurance schemes attract the interest of policyholders and insurance companies. Different types of peer-to-peer insurance have been introduced, from pure models to hybrid ones, as in the case of the broker model. In this paper, we focus on the broker model, where the groups of peers are formed by an insurance broker according to similar risk characteristics. The participants in the network pay an initial contribution defined by a cooperative rule that must be transparent and shared. A part or the whole of the collected contributions is set aside in a common fund. At the end of the year, if the common fund is sufficient to pay for the claims, the members obtain the excess over-retained premiums that is shared according to a capital allocation rule. We propose a cashback distribution mechanism based on the participant's marginal contribution to the risk, framing the issue in a cooperative game and applying the concept of Shapley value to define an optimal allocation rule of the remaining capital. A numerical application based on a portfolio of motor third-party liability policies is developed to show how the model works.