In his classical article in The American Economic Review, Arthur Raviv (1979) examines Pareto optimal insurance contracts when there are ex-post insurance costs c induced by the indemnity I for loss x. Raviv’s main result is that a necessary and sufficient condition for the Pareto optimal...

We discuss the "life cycle model" by first introducing a credit market with only biometric risk, and then market risk is introduced via risky securities. This framework enables us to find optimal pension plans and life insurance contracts where the benefits are state dependent. We compare these...

Risk-sharing in insurance is analyzed, with a view towards explaining the prevalence of deductibles. First we introduce, in a modern setting, the main concepts of the theory of risk-sharing in a group of agents. This theory we apply to the risk-sharing problem between an insurer and an insurance...