Paper: arXiv 2502.19862

Authors: Bastien Baude, Damien Challet, Ioane Muni Toke

Abstract

Decentralized lending protocols within the decentralized finance ecosystem enable the lending and borrowing of crypto-assets without relying on traditional intermediaries. Interest rates in these protocols are set algorithmically and fluctuate according to the supply and demand for liquidity. In this study, we propose an agent-based model tailored to a decentralized lending protocol and determine the optimal interest rate model. When the responses of the agents are linear with respect to the interest rate, the optimal solution is derived from a system of Riccati-type ODEs. For nonlinear behaviors, we propose a Monte-Carlo estimator, coupled with deep learning techniques, to approximate the optimal solution. Finally, after calibrating the model using block-by-block data, we conduct a risk-adjusted profit and loss analysis of the liquidity pool under industry-standard interest rate models and benchmark them against the optimal interest rate model.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a rigorous mathematical framework for optimizing interest rate models in DeFi lending protocols using stochastic optimal control, ODE systems, and deep neural network approximations. The empirical validation is strong, featuring high-frequency, block-by-block calibration on Ethereum AAVE v3 data alongside a thorough risk-adjusted PnL benchmark.

Research Flowchart

  flowchart TD
    A["Research Goal: Determine Optimal Risk-Aware Interest Rates for Decentralized Lending"] --> B["Data Input: Block-by-Block Protocol Calibration Data"]
    B --> C["Agent-Based Model Framework"]
    C --> D{"Agent Behavioral Response Type"}
    D -- "Linear Behavior" --> E["Optimal Control via Riccati-Type ODE System"]
    D -- "Nonlinear Behavior" --> F["Deep Learning + Monte-Carlo Estimator"]
    E --> G["Risk-Adjusted PnL Analysis & Benchmark against Standard Models"]
    F --> G

Cited References (45)

  1. O ptions, futures, and other derivatives (2014)
  2. D ecentralized finance: P rotocols, risks, and governance (2023)
  3. F rom banks to D e F i: T he evolution of the lending market (2022)
  4. S o K : L ending pools in decentralized finance (2021)
  5. D e F i lending: I ntermediation without information? (2022)
  6. A ave v1 (2020)
  7. A ave v2 (2020)
  8. A ave v3 (2022)
and 37 more
  1. C ompound: T he money market protocol (2019)
  2. M orpho B lue (2023)
  3. A daptive C urve I R M (2023)
  4. S ystemic fragility in decentralized markets (2022)
  5. T oxic liquidation spirals (2022) — link
  6. C ontagion in decentralized lending protocols: A case study of C ompound (2023)
  7. L iquidations: D e F i on a knife-edge (2021)
  8. A n empirical study of defi liquidations: I ncentives, risks, and instabilities (2021)
  9. T he paradox of adversarial liquidation in decentralised lending (2023)
  10. D e F i protocols for loanable funds: I nterest rates, liquidity and market efficiency (2020)
  11. T he economics of interest rate models in decentralised lending protocols (2023)
  12. A ttacks on dynamic D e F i interest rate curves (2023) — link
  13. T hinking fast and slow: D ata-driven adaptive D e F i borrow-lending protocol (2024)
  14. A gile R ate: B ringing adaptivity and robustness to D e F i lending markets (2024) — link
  15. E quilibrium in a D e F i lending market (2023)
  16. Agents’ behavior and interest rate model optimization in D e F i lending (2025)
  17. A lgorithmic and high-frequency trading (2015)
  18. D eep learning approximation for stochastic control problems (2016)
  19. D eep neural networks algorithms for stochastic control problems on finite horizon: C onvergence analysis (2021)
  20. D eep neural networks algorithms for stochastic control problems on finite horizon: N umerical applications (2022)
  21. N eural networks-based algorithms for stochastic control and P D E s in finance (2021) — link
  22. R ecurrent neural networks for stochastic control problems with delay (2021)
  23. R einforcement learning: A n introduction (2018)
  24. M ultiagent relative investment games in a jump diffusion market with deep reinforcement learning algorithm (2025)
  25. D eep reinforcement learning for market making in corporate bonds: B eating the curse of dimensionality (2019)
  26. M arket making and incentives design in the presence of a dark pool: A deep reinforcement learning approach (2019) — link
  27. R isk management with machine-learning-based algorithms (2019) — link
  28. A dam: A method for stochastic optimization (2015)
  29. T he concrete distribution: A continuous relaxation of discrete random variables (2017)
  30. D eep local volatility (2020)
  31. A generative adversarial network approach to calibration of local stochastic volatility models (2020)
  32. T he frequency distribution of the difference between two independent variates following the same P oisson distribution (1937)
  33. T he frequency distribution of the difference between two P oisson variates belonging to different populations (1946)
  34. On the P oisson difference distribution inference and applications (2010)
  35. L everaged restaking of leveraged staking: W hat are the risks? (2024)
  36. C ontinuous counterparts of P oisson and binomial distributions and their properties (2013)
  37. W hy D e F i lending? E vidence from AAVE v2 (2025)

0 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.