Reinsurance policies can be pretty bespoke; you could for instance get a policy that only covers you in the event that a tornado hits corporate HQ (=> driving corporate revenues down and healthcare costs up at the same time), or individual payments above a certain amount, or N% of aggregate claims above a certain level. You still preserve most of the benefits of self-insuring while protecting yourself against outliers, in the same way that you come out ahead if you skip insuring the loss of your refrigerator, but do insure the loss of your house.
The biggest issue is the principal-agent problem - it costs some amount to insure against once-every-20-year claims, and by that time the CEO is likely to be retired, so why buy the coverage?
That's one of the reasons why insurance companies per se are highly regulated.
The biggest issue is the principal-agent problem - it costs some amount to insure against once-every-20-year claims, and by that time the CEO is likely to be retired, so why buy the coverage?
That's one of the reasons why insurance companies per se are highly regulated.