Life insurance and pension contracts I : the time additive life cycle model

We analyze optimal consumption in the life cycle model by intro- ducing life and pension insurance contracts. The model contains a credit market with biometric risk, and market risk via risky securi- ties. This idealized framework enables us to clarify important aspects life insurance and pension contracts. We nd optimal pension plans and life insurance contracts where the bene ts are state dependent. We compare these solutions both to the ones of standard actuarial theory, and to policies o ered in practice. Implications of this include what role the insurance industry may play to improve welfare. The relationship between substitution of consumption and risk aversion is highlighted in the presence of a consumption puzzle. One problem related portfolio choice is discussed - the horizon problem. Finally, we present some comments on longevity risk and cohort risk