Work

Portfolio benchmarks in defined contribution pension plan management

Year: 2025

Type: article

Abstract: 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.

Source: Insurance Mathematics and Economics

DOI: 10.1016/j.insmatheco.2025.04.002

Authors: Daxin Huang, Yang Liu

Institutions: Hong Kong University of Science and Technology, Chinese University of Hong Kong, Shenzhen

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,270