随机利率与随机波动率环境下的DC型养老金计划

Defined-contribution pension plan with stochastic interest rate and stochastic volatility

为实现养老金的保值增值,基金管理人将养老金投资于金融市场.假设金融市场包含一种无风险资产、一种股票和一种零息票债券,其中,利率期限结构满足随机仿射利率模型,而股票价格波动率满足Heston随机波动率模型.基金管理人希望寻找一种最优投资组合以最大化其终端财富的期望效用.假设基金管理人对风险的偏好满足幂效用或指数效用,运用随机动态规划原理和变量替换方法,得到幂效用和指数效用下最优投资策略的显式解.最后,通过数值算例分析主要模型参数对最优投资策略的影响.研究结果表明,利率风险、股市波动风险以及缴费率都对缴费确定(DC)型养老金的投资决策产生较大的影响.

In order to preserve and increase the value of pension fund, a fund manager can invest pension fund into a financial market with a risk-free asset, a stock and a zero-coupon bond. In the financial market, short rate is assumed to follow stochastic affine interest rate model, while stock price is supposed to be driven by Heston’s stochastic volatility model. The fund manager expects to obtain an optimal portfolio to maximize the expected utility of terminal utility.Assuming the risk-aversion of the fund manager to satisfy power utility or exponential utility, the explicit solutions to the optimal portfolios with power utility or exponential utility are obtained by using the principle of stochastic dynamic programming and the variable change technique. Finally, a numerical example is given to analyse the impact of main market parameters on the optimal portfolios. Research results show that interest rate risk, volatility risk and contribution rate have a considerable influence on decision-making of fund manager for the defined-contribution pension found.