Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin

TL;DR

This paper determines the optimal strategy for minimizing lifetime ruin probability by investing in risky assets and purchasing deferred annuities, revealing that individuals only buy annuities if they can fully cover consumption and sustain themselves until the end of the deferral period.

Contribution

It characterizes the optimal deferred annuity purchasing strategy to minimize lifetime ruin probability, showing individuals only buy if they can cover consumption and survive until the deferral ends.

Findings

Individuals only buy deferred annuities if they can cover all consumption and survive until the end of the deferral period.

The optimal strategy involves purchasing annuities only under specific wealth and consumption conditions.

The model provides a clear criterion for when deferred annuities are optimal for lifetime ruin minimization.

Abstract

We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and can purchase a deferred annuity. Although we let the admissible set of strategies of annuity purchasing process to be increasing adapted processes, we find that the individual will not buy a deferred life annuity unless she can cover all her consumption via the annuity and have enough wealth left over to sustain her until the end of the deferral period.