Can independent underwriters benefit insurers in high-risk lines? A cournot market-game analysis

One of the greatest dangers to the solvency of property-liability insurers is writing large amounts of new business in a high-risk line (i.e., a line of insurance in which a substantial portion of buyers consists of high-risk insureds). This practice is problematic because of both potentially inadequate pricing and potentially lax underwriting. A prominent example of the latter phenomenon was the collapse of many captive insurers in the early to mid-1980s, in which the insurers relied too heavily on independent underwriters motivated solely by increasing premium volume. In this article, we employ a Cournot market-game model to study the financial impact of informed independent underwriters (i.e., unaffiliated underwriters with private information regarding the risk characteristics of insureds) on insurers in high-risk property-liability lines. In a market with a risk-neutral insurer and CARA insureds, we find that the insurer will always do worse by using a risk-neutral underwriter than by operating on a direct-writing basis. However, for an insurer employing mean-variance optimization, the proper combination of underwriter-compensation and capital allocation may lead to better outcomes than direct writing