Optimal Insurance Policies and Saving in a Temporal World

We consider Pareto optimal risk sharing between a buyer and a seller of insurance contracts, as well as consumption substitution and saving in a two-period context. The separation of the time periods allows us to consider the substitution effect. We show that the classical result of Pareto optimal risk sharing between a customer and an insurer is robust, and remains so also with recursive utility. For both expected utility and recursive utility we obtain precautionary savings with prudence. With recursive utility we identify the connection between the coefficient of elasticity of substitution in consumption and optimal saving, both under certainty and uncertainty. The separation of consumption substitution from risk aversion is shown to be partial.