The Life Cycle Model with Recursive Utility: New Insights on Pension and Life Insurance Contracts

Abstract

We analyze optimal consumption, including pensions, during the life time of a consumer using the life cycle model, when the consumer has recursive utility. The model framework is that of continuous-time with diffusion driven uncertainty. The relationship between substitution of consumption and risk aversion is highlighted, and clarified in the context of the life cycle model. We find the optimal consumption in closed form, and illustrate that the recursive utility consumer may prefer to smooth consumption shocks across time and states of the world. This agent consumes and invests to mitigate shocks to the economy, in situations where the conventional consumer is just myopic. This has consequences for what products the financial industry may choose to offer. The resulting model can be used to explain empirical puzzles for aggregates, indicating a plausible choice for the parameters of the utility function, for for the 'average' consumer in the context of life cycle model.