Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin

Details Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin

2007-03-29

arxiv.org/abs/math/0703862v2

Mathematics

Optimization and Control

Key Words: Life annuities, retirement, optimal investment, stochastic control, free boundary problem

Scientific paper

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.

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