Optimal asset allocation for DC pension subject to allocation and terminal wealth constraints under a remuneration scheme

Yinghui Dong, Mengyuan Shi and Chunrong Hua

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 3, 673-700

Abstract: We investigate the optimal investment problem faced by a defined contribution (DC) pension fund manager under simultaneous allocation and expected shortfall (ES) constraints. Under a non concave utility, a Value-at-Risk (VaR) constraint does not lead to the full prevention of moral hazard. As a widely employed risk management tool, whether an ES constraint can provide a more effective protection than a VaR constraint has been a focus point of research. We apply a dual control approach and a concavification technique to solve the ES-constrained optimization problem for a DC pension plan under an incentive scheme and derive the closed-form representations of the optimal wealth and portfolio processes. Furthermore, we compare the effect of an ES constraint on the optimal investment behavior with that under a VaR constraint in the presence of an option-like scheme for the DC pension members. Theoretical and numerical results show that for a relatively low protection level, a joint VaR and an ES constraints induce the same structure of the optimal solution, which implies that for a non concave optimization problem, the ES-based risk management has lost its advantage over the VaR-based risk management. Therefore, it needs to design a more efficient risk measure to improve the risk management for a DC pension plan.

Date: 2025
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DOI: 10.1080/03610926.2024.2316282

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