Finding Pareto Optimal Insurance Contracts

This note deals with on-line computation or learning of Pareto optimal insurance contracts. We account for the fact that the loss distribution often is unknown, unavailable, or intractable. Alternatively, the contracting parties could be inexperienced. In both cases losses must be simulated or observed, one at a time, these causing iterated revisions of the premium. The mechanical nature of probability calculus thus yields to more tentative procedures, possibly closer to how humans operate or reason in face of risk. Emphasized here is the remarkable simplicity and stability of the resulting procedures. Special attention goes to catastrophic risks and subsidized insurance.