The annuity puzzle and consumption hump under ambiguous life expectancy
Journal
Insurance: Mathematics and Economics
Journal Volume
100
Pages
76-88
Date Issued
2021
Author(s)
Han N.-W
Abstract
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. ? 2021 Elsevier B.V.
Subjects
Ambiguity aversion
Annuity
Bequest motives
Consumption hump
Robust control
Type
journal article