Time-consistent portfolio selection with monotone mean-variance preferences
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arXiv
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| Format: | Preprint |
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2025
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| author | Wang, Yike Chen, Yusha Liu, Jingzhen |
| author_facet | Wang, Yike Chen, Yusha Liu, Jingzhen |
| contents | We investigate time-inconsistent portfolio problems under a broader class of monotone mean-variance (MMV) preferences. Since the optimal strategies for MMV and mean-variance (MV) preferences coincide, the MMV optimal strategies at different initial times are necessarily time-inconsistent. To address this time-inconsistency, we consider Nash equilibrium controls of both open-loop and closed-loop types, and characterize them within a random parameter setting. The two control problems reduce to solving a flow of forward-backward stochastic differential equations and a system of extended Hamilton-Jacobi-Bellman equations, respectively. In particular, we derive semi-closed-form solutions for both types of equilibria under a deterministic parameter setting, and both solutions share the same representation, which is independent of the wealth state and the random path. We show that the investment amount under the MMV equilibrium exceeds that under the MV equilibrium, and the gap narrows over time. Furthermore, under a constant parameter setting, we find that the derived closed-loop Nash equilibrium control is a strong equilibrium strategy only when the interest rate is sufficiently large, whereas the derived open-loop Nash equilibrium control is necessarily a strong equilibrium strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-consistent portfolio selection with monotone mean-variance preferences Wang, Yike Chen, Yusha Liu, Jingzhen Optimization and Control Portfolio Management Primary: 91G10, 49N10, Secondary: 91B05, 49N90 We investigate time-inconsistent portfolio problems under a broader class of monotone mean-variance (MMV) preferences. Since the optimal strategies for MMV and mean-variance (MV) preferences coincide, the MMV optimal strategies at different initial times are necessarily time-inconsistent. To address this time-inconsistency, we consider Nash equilibrium controls of both open-loop and closed-loop types, and characterize them within a random parameter setting. The two control problems reduce to solving a flow of forward-backward stochastic differential equations and a system of extended Hamilton-Jacobi-Bellman equations, respectively. In particular, we derive semi-closed-form solutions for both types of equilibria under a deterministic parameter setting, and both solutions share the same representation, which is independent of the wealth state and the random path. We show that the investment amount under the MMV equilibrium exceeds that under the MV equilibrium, and the gap narrows over time. Furthermore, under a constant parameter setting, we find that the derived closed-loop Nash equilibrium control is a strong equilibrium strategy only when the interest rate is sufficiently large, whereas the derived open-loop Nash equilibrium control is necessarily a strong equilibrium strategy. |
| title | Time-consistent portfolio selection with monotone mean-variance preferences |
| topic | Optimization and Control Portfolio Management Primary: 91G10, 49N10, Secondary: 91B05, 49N90 |
| url | https://arxiv.org/abs/2502.11052 |