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arXiv · 2401.15659

A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation

Zongxia Liang·Keyu Zhang
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Abstract

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.

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Zongxia Liang, Keyu Zhang. 2024-01-28. A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation. https://doi.org/10.1007/s11579-024-00360-4

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