Reinsurer Risk Loads from Marginal Surplus Requirements

The return on the marginal surplus committed to support the variability of a proposed reinsurance contract is used to derive an appropriate risk load for reinsurers. The risk load is a linear combination of the standard deviation and variance of the return on the contract, and depends upon the covariance of the contract with the existing book, the standard deviation of the contract, the standard deviation of the existing book, the acceptable probability of "ruin" of the company, and the yield required on marginal surplus (the additional surplus required for this contract). A new term is defined, the reluctance to write risk, and relatively simple formulas result for it and the premium, which satisfy intuitive reasonableness criteria. Extensions to include expenses and an existing "bank" are discussed, and application is made to the interesting case of excess layer pricing. Empirical comparison suggests that the market pricing is consistent with this approach.