Monopolistic Insurance Markets Under the Coinsurance Clause

We consider a monopoly insurance company that is unable to estimate the value of covered assets at the time of underwriting. Only the distribution of the severity of losses is known. Also, an ex-post appraisal of the value of the property can be performed in case of accident. As in most property insurance lines, the premium paid relies on the value of the asset announced by the owner. The coinsurance clause stipulates that the indemnity paid by the insurer equals the actual loss multiplied by the ratio of the amount of insurance carried over the value of the insured property. We show that this clause does not allow the insurer to extract a maximum surplus from trade in the sense that policyholders would deliberately underestimate the value of their asset under that clause. We derive the monopoly equilibrium when this clause is imposed by the State using an argument of fairness among policyholders. We show that owners with a low property value will be partially insured at equilibrium, whereas owners with a larger value will be fully covered.