We establish a continuous-time model to solve the optimal consumption-saving problem with life annuity. The decision-maker has ambiguous beliefs in the force of mortality and is averse to this model uncertainty. The ambiguity aversion is represented by the max-min principle under the framework of robust control. We show that the optimal annuity demand decreases with the extent of ambiguity aversion, bequest motives, and extent of relative risk aversion. For an individual with non-zero bequest motives, the optimal annuity demand becomes zero when the extent of ambiguity aversion exceeds a certain threshold. We also show that, even if the individual has access to actuarially fair annuities, the optimal consumption would have a hump-shaped path when the individual is ambiguity-averse.

我们建立了一个连续时间模型，以解决具有年金的最佳节约能源的问题。决策者对死亡率的影响含糊不清，并且反对这种模型的不确定性。在鲁棒控制的框架下，最大-最小原理代表了歧义厌恶。我们表明，最佳年金需求随着歧义厌恶程度，遗赠动机和相对风险厌恶程度的降低而降低。对于具有非零遗赠动机的个人，当歧义厌恶程度超过某个阈值时，最佳年金需求将变为零。我们还表明，即使个人能够获得精算公平的年金，当个人避免歧义性时，最优消费也将具有驼峰状的路径。