Time discounting under uncertainty

TL;DR

This paper characterizes discounted expected utility in intertemporal decision making under uncertainty, highlighting the role of stationarity and extending to Choquet discounted utility for non-neutral attitudes.

Contribution

It provides the first complete characterization of discounted expected utility under uncertainty and introduces a generalized model incorporating hedging and non-neutral attitudes.

Findings

Strong stationarity characterizes discounted expected utility.

Weak stationarity extends the model to Choquet discounted utility.

The framework unifies attitudes towards time and uncertainty.

Abstract

We study intertemporal decision making under uncertainty. We fully characterize discounted expected utility in a framework \`a la Savage. Despite the popularity of this model, no characterization is available in this setting. The concept of stationarity, introduced by Koopmans for deterministic discounted utility, plays a central role for both attitudes towards time and towards uncertainty. We show that a strong stationarity axiom characterizes discounted expected utility. When hedging considerations are taken into account, a weaker stationarity axiom generalizes discounted expected utility to Choquet discounted expected utility, allowing for non-neutral attitudes towards uncertainty.