We present a new axiomatization of the classical discounted expected utility model, which is primarily used as a decision model for consumption streams under risk. This new axiomatization characterizes discounted expected utility as a model that satisfies natural extensions of standard axioms as in the one-period case and two additional axioms. The first axiom is a weak form of time separability. It only requires that the choice between certain constant consumption streams and lotteries should be made by just taking into account the time periods where the consumption is different. The second axiom, the time–probability equivalence, requires that risk and time preferences basically work in the same way. Moreover, we prove that preferences satisfying the natural extensions of the standard axioms as well as the first axiom can be represented in a simple form relying on three functions linked to the risk or time preferences in simple situations. Finally, we illustrate that several examples that are not fully time separable satisfy all our axioms except for the time–probability equivalence.

我们提出了经典贴现预期效用模型的新公理化，该模型主要用作风险消费流的决策模型。这种新的公理化将贴现预期效用描述为满足标准公理自然扩展的模型，如单周期情况和两个附加公理。第一公理是时间可分性的弱形式。只要求在某些恒定的消费流和彩票之间进行选择，只考虑消费不同的时间段。第二公理，时间-概率等价，要求风险和时间偏好基本上以相同的方式起作用。此外，我们证明满足标准公理和第一公理的自然扩展的偏好可以用简单的形式表示，依赖于在简单情况下与风险或时间偏好相关的三个函数。最后，我们说明了几个不完全时间可分的例子满足我们所有的公理，除了时间概率等价性。