发表机构
Università degli Studi di Udine（乌迪内大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出自适应奇点方法，用于定价和对冲含多类特征的可退保权益挂钩人寿保险合约，经理论分析与数值实验验证其有效性，揭示价值相似合约的风险敞口差异。
AI 中文摘要
我们提出一种确定性数值方法，用于定价和对冲具有周期性保费与资金缴纳、到期及死亡担保，且在相关随机波动率与随机利率下可百慕大式退保的可退保权益挂钩人寿保险合约。主要计算挑战在于与多个随机因子及提前行权耦合的非重组累积资金。我们的核心思路是避免构建完整的多维资金格：方差和利率因子在重组格上离散化，而在每个因子节点，合约价值表示为资金的自适应一维函数。周期性缴纳则作为资金变量的平移，退保通过向后障碍条件直接处理。分段三次表示传播收益和行权奇点，并通过控制表示误差的连续剪枝准则进行压缩。我们建立了金融链的弱收敛、自适应估值在表示误差消失时的收敛性，以及在规则资金区域上的Delta一致性。对于严格二叉方案，额外正则性产生一阶弱精度和支持Richardson外推的Talay-Tubaro展开。数值实验显示紧凑的表示、良好的成本-精度比，且与独立蒙特卡洛及交叉拟合最小二乘蒙特卡洛基准吻合度高。对冲结果进一步表明，价值相似的合约对权益、波动率和利率风险的敞口可能存在显著差异。
英文摘要
We propose a deterministic numerical method for pricing and hedging surrenderable equity-linked life-insurance contracts with periodic premiums and fund contributions, maturity and death guarantees, and Bermudan surrender under correlated stochastic volatility and stochastic interest rates. The main computational challenge is the non-recombining accumulated fund, which couples with multiple stochastic factors and early exercise. Our key idea is to avoid a full multidimensional fund lattice: variance and interest-rate factors are discretized on recombining lattices, while at each factor node the contract value is represented as an adaptive one-dimensional function of the fund. Periodic contributions then act as translations of the fund argument, whereas surrender is handled directly through a backward obstacle condition. Piecewise-cubic representations propagate payoff and exercise singularities and are compressed by continuous pruning criteria that control the representation error. We establish weak convergence of the financial chains, convergence of the adaptive valuation under vanishing representation error, and Delta consistency on regular fund regions. For the strict binomial scheme, additional regularity yields first-order weak accuracy and a Talay-Tubaro expansion supporting Richardson extrapolation. Numerical experiments show compact representations, favorable cost--accuracy, and close agreement with independent Monte Carlo and cross-fitted least-squares Monte Carlo benchmarks. Hedging results further show that contracts with similar values can generate materially different exposures to equity, volatility, and interest-rate risk.
