Utility function quasi-geometric discounting: a closed-form solution under the exponential

This paper studies a discrete-time utility maximization problem of an infinitely-lived quasi-geometric consumer whose labor income is subject to uninsurable idiosyncratic productivity shocks. We restrict attention to a first-order Markov recursive solution. We show that under the assumption of the exponential utility function, the problem of the quasi-geometric consumer admits a closed-form solution.