ROE, Utility and the Pricing of Risk

Actuaries, economists, underwriters, and regulators are rightly convinced that the task of pricing insurance should depend on the uncertainty of the amount and the timing of the insured losses, as well as on the correlation of those losses with those already insured. The most common approach to pricing is to allocate equity to the insurance transaction and to achieve a certain expected return on that equity. This paper will argue that this ROE approach is illogical and inconsistent, and that the proper approach is to accept no price that reduces the expected utility of the insurer. The utility-theoretic approach will enable logical and consistent pricing, and will involve no unusual practical difficulties. The paper will argue also that capital should play a role in assessing the strength of an insurer, but capital allocation should play no role in an insurer's pricing.