Optimal Investment for a Retirement Plan with Deferred Annuities

Abstract

We construct an optimal investment portfolio model with deferred annuities for an individual investor saving for retirement. The objective function consists of power utility in terms of 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. Our numerical results show that 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 realised and expected values of state variables. The optimal strategy is also compared with typical retirement plan strategies such as glide paths. Our results provide novel support for deferred annuities as a major source of retirement income.