In this paper we present a variable annuity (VA) contract embedded with a guaranteed minimum accumulated benefit rider that can be chosen to surrender the contract anytime before the maturity. In contrast to the model considered by Bernard et al. (2014), the surrender benefit in our problem is linked to the maximum value between the policyholder’s account value and the guaranteed minimum accumulated benefit. Thus, the surrender benefit of our model provides a protection against the downside risk of financial market throughout the life of contract, and thus it can be referred to as surrender guarantee. Under this circumstance with surrender guarantee, the VA contract has double surrender regions, that is, there exist two optimal surrender boundaries such that if the policyholder’s account value hits one of these boundaries, then the policyholder immediately surrenders the VA contract. Based on the Mellin transform techniques, we derive the coupled integral equations for the two optimal surrender boundaries. We solve numerically these coupled integral equations by using the recursive integration method and provide comparative statics analysis with respect to various parameters.

在本文中，我们提出了一种可变年金（VA）合同，其中嵌入有保证的最低累积收益附加条件，可以选择在到期日之前随时退回该合同。与Bernard等人所考虑的模型相反。（2014年），我们问题中的退保收益与保单持有人的账户价值和保证的最低累计收益之间的最大值挂钩。因此，我们的模型的退保利益提供了在整个合同期内抵御金融市场下行风险的保护，因此可以将其称为退保担保。在这种有退保担保的情况下，VA合同具有双重退保区域，即存在两个最优退保边界，因此，如果保单持有人的账户价值触及这些边界之一，然后，保单持有人立即放弃VA合同。基于梅林变换技术，我们导出了两个最优投降边界的耦合积分方程。我们使用递归积分方法对这些耦合积分方程进行数值求解，并针对各种参数提供比较静态分析。