This paper explores how insurance companies can coordinate to extend their joint capacity for the coverage of new and undiversifiable risks. The undiversifiable nature of such risks causes a shortage of insurance capacity and their limited knowledge makes learning and information sharing necessary. In practice, organizing such insurance supply amounts to sharing a common value divisible good between capacity constrained and privately informed insurers with a reserve price. Widely used ad-hoc co-insurance agreements out to operate as a uniform price auction with an “exit/re-entry” option. We compare it to a discriminatory auction, another auction present in the insurance industry. Both auction formats lead to different coverage/premium tradeoffs. If at least one insurer provides an optimistic expertise about the risk, ad-hoc co-insurance agreements offer higher coverage. This result is reversed when all insurers are pessimistic about the risk. Static comparative results with respect to the severity of the capacity constraints and the reserve price are provided. In the case of completely new risks, a regulator aiming at maximizing the expected coverage should promote ad-hoc co-insurance agreements when the reserve price is low enough or when competition is high enough.