AI 中文总结
本文针对均值-方差框架下考虑时变利率、缴费与死亡风险的DC养老金计划，采用鞅方法推导最优投资与保险策略，分析死亡率改善及市场参数对决策的影响，为养老金成员及计划设计提供指导。
AI 中文摘要
本文研究均值-方差框架下确定缴费型（DC）养老金计划的投资与保险策略，考虑具有时变利率、缴费和死亡风险的随机环境，允许DC计划成员决定其债券、股票配置及人寿保险保额。采用鞅方法，推导闭式最优策略与均值-方差有效前沿；进一步通过数值分析探究死亡率改善对投资与保险决策的影响，以及最优决策对市场参数的敏感性。分析表明，长寿会提升未来缴费预期，使养老金成员采取风险更低的投资策略；同时，保险策略向成年早期转移以保护未来收入的高价值，在老年阶段显著降低。此外，对目标预期财富、风险的市场价格及缴费增长进行敏感性分析，这些发现为养老金成员的投资提供实践指导，并为DC养老金计划的设计提供见解。
英文摘要
This paper studies the investment and insurance strategies of defined-contribution (DC) pension plans under the mean-variance framework. We consider a stochastic environment with time-varying interest rates, contributions, and mortality risk. The DC plan members are allowed to decide their bond and stock allocations, as well as their life insurance coverage. Adopting the martingale approach, we derive the closed-form optimal strategies and the mean-variance efficient frontier. Further numerical analysis investigates how mortality improvements affect investment and insurance decisions, as well as the sensitivity of the optimal decision to market parameters. Our analysis suggests that longevity raises expectations of future contributions, allowing pension members to adopt a less risky investment strategy. Meanwhile, insurance strategy shifts toward early adulthood to protect the high value of future income and decreases significantly at later ages. Moreover, we conduct sensitivity analyses on the target expected wealth, market price of risk, and contribution growth. These findings provide practical guidance for pension members on investment and offer insights for the design of DC pension plans.
