We construct an optimal investment portfolio model with deferred annuities for an individual investor saving in a retirement plan. The objective function consists of power utility in terms of consumption of all secured retirement income from the deferred annuity purchases, as well as bequest from remaining wealth invested in equity, bond, and cash funds. The asset universe is governed by a vector autoregressive model incorporating the Nelson–Siegel term structure and equity returns. We use multi-stage stochastic programming to solve the optimization problem numerically. Deferred annuity purchases are made continuously over the working lifetime of the investor, increasing particularly in the years before retirement. The investment strategy hedges price changes in deferred annuities, and bond holding and deferred annuity purchases increase when interest rates are high. Optimal investment and deferred annuity choices depend on realized and expected values of state variables. The optimal strategy is also compared with typical retirement plan strategies such as glide paths. Our results provide support for deferred annuities as a major source of retirement income.

我们构建了具有递延年金的最优投资组合模型，用于个人投资者节省退休计划。目标函数由电力公用事业构成，包括消耗所有从延期年金购买中获得的有担保退休收入，以及从股票，债券和现金基金中剩余的财富中获得的遗产。资产领域由矢量自回归模型控制，该模型结合了Nelson-Siegel的期限结构和股票收益。我们使用多阶段随机规划来数值求解优化问题。延期年金的购买是在投资者的整个工作寿命中连续进行的，尤其是在退休前的几年中。该投资策略可对冲年金价格的变化，利率高时，债券持有量和递延年金购买量增加。最优投资和递延年金选择取决于状态变量的已实现值和期望值。还将最佳策略与典型的退休计划策略（例如滑行路径）进行比较。我们的结果为递延年金作为退休收入的主要来源提供了支持。