تقرير
A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation
| العنوان: | A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation |
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| المؤلفون: | Liang, Zongxia, Zhang, Keyu |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Quantitative Finance |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Quantitative Finance - Mathematical Finance |
| الوصف: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:2206.13341 by other authors |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s11579-024-00360-4 |
| URL الوصول: | http://arxiv.org/abs/2401.15659 |
| رقم الأكسشن: | edsarx.2401.15659 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s11579-024-00360-4 |
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