Variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) entitle the policy holder to periodic withdrawals together with a terminal payoff linked to the performance of an equity fund. In this paper, we consider the valuation of a general class of GMWB annuities, allowing for step-up, bonus and surrender features, taking also into account mortality risk and death benefits. When dynamic withdrawals are allowed, the valuation of GMWB annuities leads to a stochastic optimal control problem, which we address here by dynamic programming techniques. Adopting a Hull-White interest rate model, correlated with the equity fund, we propose an efficient tree-based algorithm. We perform a thorough analysis of the determinants of the market value of GMWB annuities and of the optimal withdrawal strategies. In particular, we study the impact of a low/negative interest rate environment. Our findings indicate that low/negative rates profoundly affect the optimal withdrawal behaviour and, in combination with step-up and bonus features, increase significantly the fair values of GMWB annuities, which can only be compensated by large management fees.

具有保证最低提款福利（GMWB）的可变年金使保单持有人有权定期提款以及与股票基金业绩挂钩的最终收益。在本文中，我们考虑了一般类别 GMWB 年金的估值，考虑到递增、红利和退保功能，同时还考虑了死亡风险和死亡抚恤金。当允许动态提款时，GMWB 年金的估值会导致随机最优控制问题，我们在这里通过动态规划技术来解决这个问题。采用与股票基金相关的赫尔-怀特利率模型，我们提出了一种高效的基于树的算法。我们对 GMWB 年金市场价值的决定因素和最佳提款策略进行了全面分析。尤其，我们研究低/负利率环境的影响。我们的研究结果表明，低/负利率深刻影响最佳提款行为，并与递增和红利功能相结合，显着增加了 GMWB 年金的公允价值，而这只能通过大量管理费来补偿。