mlsanityData to 7 Oct 2026

A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents

arXiv 2402.07365 ↗First posted 12 Feb 2024math.OC cs.GT cs.LGcited by 0

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Abstract (arXiv)

Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a graphon. In this paper, we focus on a graphon game for optimal investment under relative performance criteria, and we propose a deep learning method. The method builds upon two key ingredients: first, a characterization of Nash equilibria by forward-backward stochastic differential equations and, second, recent advances of machine learning algorithms for stochastic differential games. We provide numerical experiments on two different financial models. In each model, we compare the effect of several graphons, which correspond to different structures of interactions.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 24 of its 58 references that are in the map. First posted on arXiv 12 Feb 2024.

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References · 24

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  2. 2020Graph Neural Networks: Architectures, Stability and Transferabilitycited by 79
  3. 2018Convergence of the Deep BSDE Method for Coupled FBSDEscited by 42
  4. 2020Learning Graphons via Structured Gromov-Wasserstein Barycenterscited by 36
  5. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Casecited by 34
  6. 2017Rates of Convergence of Spectral Methods for Graphon Estimationcited by 28
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  10. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  11. 2019Numerical resolution of McKean-Vlasov FBSDEs using neural networkscited by 19
  12. 2019Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learningcited by 15
12 more
  1. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  2. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  3. 2019Stochastic Graphon Games: I. The Static Casecited by 12
  4. 2021Finite State Graphon Games with Applications to Epidemicscited by 9
  5. 2018Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testingcited by 8
  6. 2020A posteriori error estimates for fully coupled McKean-Vlasov forward-backward SDEscited by 4
  7. 2022A label-state formulation of stochastic graphon games and approximate equilibria on large networkscited by 4
  8. 2023A Machine Learning Method for Stackelberg Mean Field Gamescited by 4
  9. 2019Many-player games of optimal consumption and investment under relative performance criteriacited by 3
  10. 2021N-player and Mean-field Games in Ito-diffusion Markets with Competitive or Homophilous Interactioncited by 3
  11. 2022Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactionscited by 2
  12. 2015Portfolio Optimization under Nonlinear Utilitycited by 1

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