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 |
---|---|
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 |
---|