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

• Published in: Communications in statistics. Theory and methods Vol. 54; no. 3; pp. 673 - 700
• Main Authors: Dong, Yinghui, Shi, Mengyuan, Hua, Chunrong
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 01.02.2025; Taylor & Francis Ltd
• Subjects: closed convex cone; concavification; Constraints; DC pension; Defined contribution plans; dual control; ES constraint; Optimization; Pension plans; Risk management
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2024.2316282

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.