Reinsurance Arrangements Minimizing the Total Required Capital

Reinsurance reduces the required capital of the primary insurer but in-creases that of the reinsurer. Capital is costly. All capital costs, including that of the reinsurer, are ultimately borne by primary policyholders. Reducing the total capital of insurers and reinsurers lowers the total capital cost and the total primary policy premium. A reinsurance arrangement is considered optimal if it minimizes the total required capital. This optimal reinsurance is shown to be an attracting equilibrium under price competition. Evidence suggests that there is an inverse relationship between the total required capital and the correlation between the losses held by dierent insurers. Examples are constructed to support this observation.

Keywords. Required capital, capital cost, optimal reinsurance, subadditive risk measure, correlation between losses