Long Dated Life Insurance and Pension Contracts

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 solutions both to the ones of standard actuarial theory, and to policies offered in practice. Two related portfolio choice puzzles are discussed in the light of recent research, one is the horizon problem, the other is related to the aggregate market data of the last century, where theory and practice diverge. Finally we present some comments on longevity risk and cohort risk.