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

Zongxia Liang and Keyu Zhang

Papers from arXiv.org

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.

Date: 2024-01
New Economics Papers: this item is included in nep-gth
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