Underwriting Risk

In a competitive insurance market, insurers have limited influence on the premium charged for an insurance contract. They must decide whether or not to compete at the market price. This paper deals with one factor in this decision – risk. From policyholder’s standpoint, the only risk that matters is insurer insolvency. For the insurer to stay in business, it has to have sufficient capital to keep this risk below an acceptable level. Also, investors demand an acceptable return on this capital. The problem is that the return comes from premiums that are charged to individual insureds, each with their own risk characteristics. This paper proposes a way to set standards for accepting individual insureds based on the risk each contributes to the insurer’s portfolio. These standards will assign the marginal capital to the insured. These standards will be expressed in terms of the acceptable return on allocated surplus. They will take into account: (1) the variability of the insurer’s loss; (2) the time it takes until all claims are paid; and (3) the correlation of the insured’s losses with the insurer’s other losses. We start by illustrating the basic concepts with simple examples, and finish with a comprehensive example that shows how we can put these standards into practice.