Portfolio benchmarks in defined contribution pension plan management
研究了确定缴费型养老金计划中引入投资组合基准的最优投资问题，提出了参数化勒让德变换和蒙特卡洛二分法解决技术难题，并发现高漂移基准会导致相反的风险行为。
In financial practice, a portfolio benchmark is of importance as it characterizes the fluctuation of the market and better evaluates the performance of the fund manager. We study the optimal investment problem of Defined Contribution (DC) pension plan management with portfolio benchmarks. As such, three technical difficulties arise, and we overcome them accordingly. First, the classic Legendre transformation cannot handle the stochastic nature of the portfolio benchmark. We introduce a parameterized Legendre transformation technique and conduct it to obtain closed-form optimal control strategies. Second, we discover that the optimal solution is not unique when the drift parameter of the benchmark is exactly Merton's constant. We employ a risk management criterion minimizing the liquidation probability to further select a “best” control strategy among the optimums. Third, the Lagrange multiplier cannot be directly solved from the budget constraint. We propose a new numerical technique called the Monte Carlo bisection method to solve it. Therefore, we can analyze the optimal strategies with asymptotic analysis and demonstrate financial insights. We find that when the benchmark is deterministic or its drift is low, the optimal investment aligns with the literature, while the high-drift benchmarks lead to an opposite risk behavior. Finally, empirical validation using the US and Chinese market data shows that our strategy is more effective in a lower risk-premium market.