关键词: DC型养老金, 均衡投资策略, 保费返还条款, 通胀风险

Abstract: Nowadays, the pension gap is growing large with the deepening of the global aging. Hence, it is quite urgent to investigate the investment management of pension funds. As the defined contribution (DC) pension plan has an advantage in easing the pressure of the social security system by transferring the investment risk and longevity risk from sponsors to pension members, it has become the direction of the global pension system reform. Therefore, the asset allocation for DC pension plans has attracted much attention in recent years. Mean-variance model (MARKOWITZ,1952) can balance the returns and risks of investment, which makes it an important criterion to study the asset allocation for DC pension funds. However, because the “variance” term in the mean-variance objective function is nonlinear, the mean-variance criterion lacks the iterated expected property. Thus, the optimal investment strategy under the mean-variance criterion (known as the pre-commitment investment strategy) is not time-consistent. Nevertheless, rational investors want to obtain an optimal strategy at any time point, i.e., the time-consistent strategy. It is gratifying that some scholars used game theoretical approach to deal with the time-inconsistent optimization problem and obtained a so-called equilibrium investment strategy, which is the desired time-consistent investment strategy. Drawing on this method, we study the equilibrium investment strategy for DC pension funds in our work.
To protect the rights of pension members who die before retirement, we introduce a return of premiums clause: all of the premiums contributed by dead members can be withdrawn by their heirs. We assume that the financial market consists of one risk-free asset and multiple risky assets. Since the time horizon of the pension plan is generally very long, it is also necessary to consider the impact of the inflation risk. Firstly, in the non-cooperative game framework, the equilibrium strategy is defined. Secondly, using the extended Bellman equation and matrix representation techniques, we obtain the analytical expressions for the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier. Thirdly, two special cases of our model are discussed. Finally, using numerical examples based on real data from the Chinese market, we analyze the impact of inflation risk and return of premiums clauses on the equilibrium investment strategy and the corresponding efficient frontier.
The theoretical results show that: (1)at any time, the pension manager will invest less wealth in the risky assets if his risk aversion level becomes larger; (2)at any time, the well-known two funds separation theorem holds; (3)the equilibrium investment strategy at any time depends on the current wealth and the return of premiums clause. Compared with previous studies (e.g. BIAN et al., 2018), this result is more practical.
The numerical results show that: (1)considering the return of premiums clause will make the pension manger more cautious about investing in risky assets; (2)if the inflation risk is ignored, the purchasing power of the normal wealth will be overestimated, which is adverse to the financial planning of the pension plan; (3)to obtain the same expected terminal wealth, the pension manager faces more risk when the return of premiums clause and the inflation risk are considered.

Key words: DC pension funds, equilibrium investment strategy, return of premiums clause, inflation risk