VaR 约束下 DC 养老金的最优投资问题
Optimal Investment of DC Pension Plans under VaR Constraint
DOI: 10.12677/AAM.2025.143131, PDF,    科研立项经费支持
作者: 高淑萍：河北工业大学理学院，天津
关键词: DC养老金；通货膨胀；VaR约束；鞍方法；Lagrange对偶理论；DC Pension； Inflation； VaR Constraint； Martingale Method； Lagrange Dual Method
摘要: 本文研究了带有 VaR (Value-at-Risk, 风险价值)约束的固定缴费(defined contribution, DC) 型养老金的最优投资问题。 基金管理者将基金账户财富投资于由无风险资产，指数债券以及股票 所组成的金融市场中, 其目标为使得终端财富在 VaR 约束下的预期效用最大化。 本文模型考虑随 机的通货膨胀环境以及随机的薪资过程，风险资产的漂移项为随机变量，风险市场价格具有已知 的概率分布。 首先引入辅助过程, 将原问题转化为自融资问题。 然后应用 Lagrange 对偶理论和鞍 方法, 推导得到了 CRRA 效用下的最优投资策略。
Abstract: This paper investigates an optimal investment problem of defined contribution (DC) pension with VaR (Value-at-Risk) constraint. The fund managers invest his wealth in a financial market consisting of a risk-free asset, a stock and an index bond, with the objective of maximizing the expected utility of terminal wealth under VaR constraint. In this model, we take account into stochastic inflation and salary process. The drift terms of the risky assets are described by random variables, and the market price of risk has a known probability distribution. We first introduce an auxiliary process to transform the original problem into a self-financing optimization problem. Then using the Lagrange dual method and martingale method, we derive the optimal investment strategy under CRRA utility.
文章引用：高淑萍. VaR 约束下 DC 养老金的最优投资问题[J]. 应用数学进展, 2025, 14(3): 450-466. https://doi.org/10.12677/AAM.2025.143131

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