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Self-annuitization and ruin in retirement. With discussion. (English) Zbl 1083.60515

Summary: At retirement, most individuals face a choice between voluntary annuitization and discretionary management of assets with systematic withdrawals for consumption purposes. Annuitization ‘buying a life annuity from an insurance company’ assures a lifelong consumption stream that cannot be outlived, but it is at the expense of a complete loss of liquidity. On the other hand, discretionary management and consumption from assets ‘self-annuitization’ preserves flexibility but with the distinct risk that a constant standard of living will not be maintainable. We compute the lifetime and eventual probability of ruin (PoR) for an individual who wishes to consume a fixed periodic amount ‘a self-constructed annuity’ from an initial endowment invested in a portfolio earning a stochastic (lognormal) rate of return. The lifetime PoR is the probability that net wealth will hit zero prior to a stochastic date of death. The eventual PoR is the probability that net wealth will ever hit zero for an infinitely lived individual.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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