4/2随机波动率模型下带有最低担保的动态均值-方差 DC型养老金计划

Dynamic mean-variance asset allocation for a DC pension plan with the minimum guarantee under 4/2 stochastic volatility model

  • 摘要: 文章在均值-方差框架下研究了具有4/2随机波动率和最低年金担保的缴费确定(DC)型养老金的最优投资问题。基金管理者可以将养老金财富投资于由一种无风险资产、一种零息债券和一种风险资产构成的金融市场,其中利率期限结构服从仿射利率模型,而风险资产的价格过程服从带有随机利率的4/2随机波动率模型。假设最低担保水平与瞬时利率相关,以终端财富超过最低担保的盈余过程的方差为目标建立均值-方差模型。通过构建辅助过程,将初始问题转化为等价的自融资投资问题,运用拉格朗日对偶定理和随机最优控制理论推导出了有效策略和有效前沿的闭式解。最后,通过数值算例分析了模型参数对有效策略和有效前沿的影响。

     

    Abstract: This paper investigates the optimal investment problem for the defined contribution (DC) pension plan with 4/2 stochastic volatility the and minimum annuity guarantee in a mean-variance framework. The fund manager is allowed to invest pension wealth in a financial market consisting of a risk-free asset, a zero-coupon bond and a stock, where the interest rate term structure follows the affine interest rate model and the stock price process follows the 4/2 stochastic volatility model with stochastic interest rate. Assuming that the minimum guarantee level is correlated with the instantaneous interest rate, a mean-variance model is developed with the objective of the variance of the surplus process in which the terminal wealth exceeds the minimum guarantee. By constructing an auxiliary process, the initial problem is transformed into an equivalent self-financing investment problem, and closed-form solutions for the efficient strategy and efficient frontier are derived using Lagrange duality theorem and stochastic optimal control theory. Finally, the effects of model parameters on the efficient strategy and efficient frontier are analyzed by numerical examples.

     

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