Optimal Reversible Annuities to Minimize the Probability of Lifetime Ruin

TL;DR

This paper determines the optimal strategies for purchasing and surrendering reversible life annuities to minimize the probability of lifetime ruin, considering market assets and surrender charges, under different asset constraints.

Contribution

It introduces a model for optimal reversible annuity strategies accounting for surrender charges and asset constraints, providing explicit strategies and insights into their dependence on market conditions.

Findings

Individuals will not buy annuities unless they can cover all consumption when they can buy or sell freely.

In the non-negative asset case, individuals surrender just enough to keep assets positive.

Large surrender charges discourage annuity purchase unless covering all consumption.

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 who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; or (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexiblity to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual's annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.