The economics of risk sharing in discrete time with translation invariant recursive utility

Abstract

We consider optimal risk sharing in a dynamic setting, where agents have preferences represented by translation invariant recursive utility. This model has some appealing features, both compared to the scale invariant one and to the standard model with expected utility. First, the model allows for a treatment of heterogeneous preferences. This leads to extensions in more realistic directions of the standard, one-period risk sharing model. Second, the new endogenous variable entering the state price deflator is a traded security, an annuity, while in the scale invariant model the corresponding variable is the agent’s wealth. The model invites for a closer look at the mutuality principle in syndicates and optimal risk sharing in society. We also embed a stock market in our setting and derive a consumption based capital asset pricing model