We operationalise the theoretical modelling of Marín-Solano and Jorge Navas (2010), seeking to understand the consequences for optimal consumption, life insurance and annuity demand in a time inconsistent world, by incorporating the insurance insights from Richard (1975). Richar, in particular, has an elegant treatment of optimal annuity demand, rarely harnessed in the literature. Central to Richard's creation of demand for personal insurance is a bequest motive and, in addition to implementing time inconsistency through hyperbolic discounting, our analysis is further expanded to include naïve and sophisticated agents with a luxury bequest motive (Lockwood, 2012). Compared to a more simplistic ‘necessity’ bequest framework, luxury bequests (broadly) weaken optimal life insurance demand and strengthen optimal life annuity demand for the less wealthy. In contrast, time inconsistency offers a wide spectrum of outcomes, and our modelling, calibrated to Swiss data, contributes to understanding the annuity puzzle—observed low levels of (voluntary) purchases of life annuities.
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- Annuity puzzle
- Dynamic programming
- Hyperbolic discounting
- Luxury bequests