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...

In the canonical model of investments, the optimal fractions in the risky assets do not depend on the time horizon. This is against empirical evidence, and against the typical recommendations of portfolio managers. We demonstrate that if the intertemporal coefficient of relative risk aversion is...

Interest rate guarantees seem to be included in life insurance and pension products in most countries. The exact implementations of these guarantees vary from country to country and are often linked to different distribution of investment surplus mechanisms. In this paper we first attempt to...