On the Unfairness of Actuarial Fair Annuities

Actuarial fairness pertains to the situation in which the price of an insurance contract is equal to its expected outcome. This paradigm is at odds with financial pricing: If two financial contracts have the same expected value, but one is better than the other in the sense of second order stochastic dominance, then the better contract will be strictly more expensive. We show that actuarial fairness leads to unfairness in that annuitants with higher survival rates have a better payoff than those with lower survival rates. To deal with this issue we propose equal utility pricing, i.e., we determine prices such that all contracts have the same (nonlinear) utility from the viewpoint of a third party (e.g., a social planner). This approach is of particular relevance with respect to the fair design of group self annuitization