The merits of pooling claims: Mutual vs. stock insurers

This paper identifies combinations of premiums, equity capital contributions, default probabilities, and pool sizes, under which a risk-averse policyholder is indifferent between purchasing insurance coverage with a mutual or a shareholder insurance company. We analyze in a first step the combinations of premiums and equity contributions within a fixed pool size, such that a policyholder is indiferent to either of the two legal forms. In a second step, we include the restriction of a fixed default probability in both the mutual and shareholder insurance companies. A numerical illustration is provided; given a fixed default probability, a determined pool size and fair premiums (i.e., the premium equals the expected indemnity payments), a policyholder in the shareholder company experiences higher utility levels than a policyholder in a mutual insurance company. Hence, a risk-averse policyholder accepts an unfair premium in the shareholder company to obtain the same utility level provided by the mutual company.