Dynamic learning for a DC pension plan with random risk aversion

Jiaqi Qian; Jiaming Su; Yongqiao Wang; Jiaqi Qian; Jiaming Su; Yongqiao Wang

doi:10.3934/jimo.2026160

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 9: 4599-4626. doi: 10.3934/jimo.2026160

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Research article

Dynamic learning for a DC pension plan with random risk aversion

School of Finance, Zhejiang Gongshang University, 18, Xuezheng Street, Hangzhou 310018, Zhejiang, China

Received: 03 June 2026 Revised: 14 August 2026 Accepted: 20 August 2026 Published: 28 August 2026
Primary: 93E20, 91B30; Secondary: 93E11, 91B16

This paper investigated the equilibrium investment strategy for a defined contribution (DC) pension plan that incorporates random risk aversion and stock return predictability. The financial market consists of a risk-free asset, an inflation-indexed bond, and a stock, where the expected stock return is driven by an unobservable mean-reverting predictor. By filtering techniques, a DC member dynamically learns and updates the estimation of this unobservable predictor based on the observations. Different from previous studies that consider only random risk aversion and resort to a system of ordinary differential equations (ODEs), this paper further incorporated stock return predictability and characterized the equilibrium strategy as a system of partial differential equations (PDEs). In the case of power utility, we derived the semi-closed form of the equilibrium investment strategy as the solution of a PDE system, and verified the existence of the solution by the Banach fixed-point theorem. Rigorous analysis showed that ignoring either random risk aversion or stock return predictability leads to welfare loss. Numerical analysis confirmed the welfare loss.
- DC pension plan,
- random risk aversion,
- certainty equivalents,
- stock return predictability,
- learning
Citation: Jiaqi Qian, Jiaming Su, Yongqiao Wang. Dynamic learning for a DC pension plan with random risk aversion[J]. Journal of Industrial and Management Optimization, 2026, 22(9): 4599-4626. doi: 10.3934/jimo.2026160

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Abstract

This paper investigated the equilibrium investment strategy for a defined contribution (DC) pension plan that incorporates random risk aversion and stock return predictability. The financial market consists of a risk-free asset, an inflation-indexed bond, and a stock, where the expected stock return is driven by an unobservable mean-reverting predictor. By filtering techniques, a DC member dynamically learns and updates the estimation of this unobservable predictor based on the observations. Different from previous studies that consider only random risk aversion and resort to a system of ordinary differential equations (ODEs), this paper further incorporated stock return predictability and characterized the equilibrium strategy as a system of partial differential equations (PDEs). In the case of power utility, we derived the semi-closed form of the equilibrium investment strategy as the solution of a PDE system, and verified the existence of the solution by the Banach fixed-point theorem. Rigorous analysis showed that ignoring either random risk aversion or stock return predictability leads to welfare loss. Numerical analysis confirmed the welfare loss.

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