Article Contents
Article Contents

# Robust optimal strategies of DC pension plans with stochastic volatility and stochastic income under mean-variance criteria

• * Corresponding authors: Hao Chang and Hui Zhao

This research is supported by the National Natural Science Foundation of China (Nos.71671122 and 11771329)

• This paper studies a robust optimal investment problem under the mean-variance criterion for a defined contribution (DC) pension plan with an ambiguity-averse member (AAM), who worries about model misspecification and aims to find robust optimal strategy. The member has access to a risk-free asset (i.e., cash or bank account) and a risky asset (i.e., the stock) in a financial market. In order to get closer to the actual environment, we assume that both the income level and stock price are driven by Heston's stochastic volatility model. A continuous-time mean-variance model with ambiguity aversion for a DC pension plan is established. By using the Lagrangian multiplier method and stochastic optimal control theory, the closed-form expressions for robust efficient strategy and efficient frontier are derived. In addition, some special cases are derived in detail. Finally, a numerical example is presented to illustrate the effects of model parameters on the robust efficient strategy and the efficient frontier, and some economic implications have been revealed.

Mathematics Subject Classification: Primary: 60H30, 91B28; Secondary: 93E20.

 Citation:

• Figure 1.  The effects of volatility parameters $\alpha$, $\sigma _0$, $\lambda _S$ and $\rho$ on $\pi ^{\ast }\left( t \right)$

Figure 2.  The effects of income parameters $\mu$, $\sigma _1$ and $k$ on $\pi ^ {\ast }\left( t \right)$

Figure 3.  The effect of ambiguity-aversion coefficient $\beta$ on $\pi ^ {\ast }\left( t \right)$

Figure 4.  The effects of volatility parameters $\alpha$ and $\sigma _0$ on $\sigma \left( {X\left( T \right)} \right)$

Figure 5.  The effects of income parameters $\mu$ and $k$ on $\sigma \left( {X\left( T \right)} \right)$

Figure 6.  The effect of ambiguity-aversion coefficient $\beta$ on $\sigma \left( {X\left( T \right)} \right)$

Figure 7.  Comparisons of the efficient strategies and the efficient frontiers

Figure 8.  When $\rho = -0.65$ and $\lambda _S = 1.5$, we have $\Delta>0$; when $\rho = -0.87$ and $\lambda _S = 12.56$, we get $\Delta = 0$; when $\rho = -0.9$ and $\lambda _S = 10$, we have $\Delta<0$. The effects of different symbols of $\Delta$ on $\pi ^ {\ast }(t)$ and $\sigma (X(T))$

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