  The peer-to-peer (P2P) economy has been growing with the advent of the
Internet, with well known brands such as Uber or Airbnb being examples thereof.
In the insurance sector the approach is still in its infancy, but some
companies have started to explore P2P-based collaborative insurance products
(eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only
recently started to consider those risk sharing mechanisms, as in Denuit and
Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a
P2P product, with some reciprocal risk sharing contracts. Here, we consider the
case where policyholders still have an insurance contract, but the first
self-insurance layer, below the deductible, can be shared with friends. We
study the impact of the shape of the network (through the distribution of
degrees) on the risk reduction. We consider also some optimal setting of the
reciprocal commitments, and discuss the introduction of contracts with friends
of friends to mitigate some possible drawbacks of having people without enough
connections to exchange risks.
