Optimal investment and consumption under forward utilities with relative performance concerns
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914468185767936 |
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| author | Broux-Quemerais, Guillaume Matoussi, Anis Chao, Zhou |
| author_facet | Broux-Quemerais, Guillaume Matoussi, Anis Chao, Zhou |
| contents | We study a n-player and mean-field portfolio optimization problem under relative performance concerns with non-zero volatility, for wealth and consumption. The consistency assumption defining forward relative performance processes leads to a sufficient characterization of such processes with mean of a Stochastic HJB equations, which highlights the link between wealth and consumption utility, and also characterizes the optimal strategies. In particular, forward relative performance processes with a wealth utility of CRRA type and separable time and space dependence necessarily have a consumption utility of the same form, with the same risk aversion parameter. This characterization gives a better understanding of the drift condition ensuring time consistency. In this setting, we establish closed form of the Nash equilibrium for both the n-player and mean eld problems. We also provide some numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal investment and consumption under forward utilities with relative performance concerns Broux-Quemerais, Guillaume Matoussi, Anis Chao, Zhou Optimization and Control Probability We study a n-player and mean-field portfolio optimization problem under relative performance concerns with non-zero volatility, for wealth and consumption. The consistency assumption defining forward relative performance processes leads to a sufficient characterization of such processes with mean of a Stochastic HJB equations, which highlights the link between wealth and consumption utility, and also characterizes the optimal strategies. In particular, forward relative performance processes with a wealth utility of CRRA type and separable time and space dependence necessarily have a consumption utility of the same form, with the same risk aversion parameter. This characterization gives a better understanding of the drift condition ensuring time consistency. In this setting, we establish closed form of the Nash equilibrium for both the n-player and mean eld problems. We also provide some numerical examples. |
| title | Optimal investment and consumption under forward utilities with relative performance concerns |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2506.22514 |