The Impact of reinsurance on the cost of capital

The impact of reinsurance on the economic capital and the cost of capital is examined. The effectiveness of alternative reinsurance forms is measured by comparing the corresponding risk-adjusted returns on capital and the costs of capital associated to the retained insurance risk. With respect to these decision criteria, it is shown for a life insurance portfolio that the limited stop-loss reinsurance is preferred to the excess-of-loss reinsurance. Several results of independent interest are obtained. It is shown how solvability can always be achieved using the limited stop-loss reinsurance form. Two inequalities for the loading factor of the excess-of-loss and stop-loss reinsurance premiums are derived. A new justification of the gamma approximation to the aggregate claims distribution is proposed, which leads to value-at-risk upper bounds.

Keywords : solvency risk, economic capital, cost of capital, RAROC, value-at-risk, excess-of-loss, limited stop-loss