Dynamic economics with quantile preferences

This paper studies a dynamic quantile model for intertemporal decisions under uncertainty, in which the decision maker maximizes the $\tau$-quantile of the stream of future utilities, for $\tau\in (0,1)$. We present two sets of contributions. First, we generalize existing results in directions that are important for applications. In particular, the sets of choices and random shocks are general metric spaces, either connected or finite. Moreover, the future state is not exclusively determined by agent's choice, but can also be influenced by shocks. Under these generalizations, we establish the Principle of Optimality, show that the corresponding dynamic problem yields a value function and, under suitable assumptions, this value function is concave and differentiable. Additionally, we derive the corresponding Euler equation. Second, we illustrate the usefulness of this approach by studying two prominent dynamic economics models. The first deals with intertemporal consumption with one asset. We obtain closed form expressions for the value function, the optimal asset allocation and consumption, as well as for the consumption path. These closed form solutions allow us to obtain useful comparative statics that shed light on how consumption and savings respond to increase in risk aversion, impatience and interest rates. For the second model, we discuss a quantile-based version of the job-search model with uncertainty.