The name is absent

4 “Insuring” Non-Verifiable Losses with Brokers

In the bilateral model above, the policyholder could hold up the insurer for a payment against the non-
verifiable loss, by threatening to withdraw his/her future business. This implies that, for the hold up to
result in a positive transfer, future rents must be strictly positive. Indeed, the risk averse policyholder is
willing to endow the insurer with positive rent in order to create a mechanism to hedge the non-verifiable
loss as long as the interest rate is not too high.

The problem with this model is that it results in either a very small transfer, because future profits on the
policy are small, or that the policyholder must bestow very large rents on the insurer in order to get a useful
level of coverage for potentially large losses. In principal, we can mitigate this trade off between coverage
and rent, by changing the information assumptions. Instead of allowing only the policyholder to observe
the settlement, b, we allow all transfers to be observed by all the insurer’s policyholders. With similar
assumptions about beliefs, (i.e., all policyholders upgrade (downgrade) their priors about future settlements,
when the incumbent makes (fails to make) a settlement of bζ_r ) then all the firm’s policyholders would switch
insurers if the insurer failed to pay b_br for any one of them suffering a loss. This increases the hold up power
of the claimant which allows larger coverage to be obtained for non-verifiable losses, whilst keeping the rent
contribution in each premium fairly low.

The enhanced model outlined in the previous paragraph suggests that brokers may not be strictly nec-
essary to create a market for non-verifiable losses. However, the informational assumptions are strong; all
policyholders must observe all of the incumbent insurers claim payments to all policyholders and be prepared
to switch if even one policyholder is denied. We clearly need some coordination mechanism to harness the
hold-up power of multiple policyholders, while permitting the insurer to extract rents for exposing itself to
this ex-post hold up. We present the insurance broker as the coordinating device.

There are multiple agents of three types: risk-averse policyholders, risk-neutral insurers, and brokers.
Each policyholder initially secures a broker to arrange insurance and offers a compensation, k, to the broker
which we assume to be a linear function of the insurer’s rent. This compensation ensures that the broker has
an ex ante interest in securing an incomplete contract with expectations of a settlement for non-verifiable
losses (recall that these rents provide the ex post hold up power from which the settlement is made).
Suppose that each broker arranges incomplete contracts between m such policyholders and an incumbent
insurer. Such contracts will offer explicit coverage of c*_br for verifiable losses and an expected settlement of

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