Optimal life-cycle labour supply, consumption, and investment: The role of longevity-linked assets

We solve in closed form the problem of an agent who maximises his inter-temporal lifetime utility. The agent is subject to the so-called longevity risk, i.e. his force of mortality is stochastic. His utility is additively separable on leisure (while working) and consumption. Consumer's preferences belong to the Hyperbolic Absolute Risk Aversion family, with a subsistence consumption level. The individual optimally chooses labour supply, consumption, and portfolio allocation. We study these optimal choices when the agent has access to a complete financial market, where he can trade in longevity-linked securities. He can also contribute to a personal pension scheme. A calibrated application shows that the optimal demand for the longevity-linked assets crucially depends on the stages of the agent's life and his wage profiles. This observation opens up the possibility of longevity risk transfers across individuals with heterogeneous characteristics.