Paper: arXiv 2503.18237

Authors: Tarun Chitra

Abstract

Lending within decentralized finance (DeFi) has facilitated over $100 billion of loans since 2020. A long-standing inefficiency in DeFi lending protocols such as Aave is the use of static pricing mechanisms for loans. These mechanisms have been shown to maximize neither welfare nor revenue for participants in DeFi lending protocols. Recently, adaptive supply models pioneered by Morpho and Euler have become a popular means of dynamic pricing for loans. This pricing is facilitated by agents known as curators, who bid to match supply and demand. We construct and analyze an online learning model for static and dynamic pricing models within DeFi lending. We show that when loans are small and have a short duration relative to an observation time $T$, adaptive supply models achieve $O(\log T)$ regret, while static models cannot achieve better than $Ω(\sqrt{T})$ regret. We then study competitive behavior between curators, demonstrating that adaptive supply mechanisms maximize revenue and welfare for both borrowers and lenders.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly novel theoretical framework modeling DeFi lending protocol pricing generations as an online convex optimization problem. It establishes formal theoretical regret bounds (O(log T) vs Omega(sqrt(T))) for dynamic versus static interest rate pricing models, though it relies purely on theoretical proofs rather than empirical backtesting on chain data.

Research Flowchart

  flowchart TD
    A["Research Question: Can dynamic pricing outperform static models in DeFi lending?"] --> B["Inputs: Historical Loan Data & Protocol Parameters (Aave, Morpho, Euler)"]
    B --> C["Online Learning Model Construction"]
    C --> D["Comparative Regret & Competition Analysis"]
    D --> E["Findings: Dynamic Models achieve O(log T) Regret vs. static Ω(√T)"]
    D --> F["Outcomes: Curator competition maximizes revenue & welfare for users"]

Cited References (179)

  1. The C omprehensive T ex A rchive N etwork ( CTAN ) (1993)
  2. Diabetes (2023) — link
  3. A study on AMMs for trading fixed yield and Pendle V2’s Principal Token AMM (2022)
  4. Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms (2009)
  5. A ratings-based model for credit events in makerdao (2019)
  6. Succinct Network: Prove the World’s Software (2024)
  7. Introduction to online nonstochastic control (2022) — link
  8. Allocation problems in ride-sharing platforms: Online matching with offline reusable resources (2021)
and 171 more
  1. Optimal dynamic regret in LQR control (2022)
  2. Online learning with low rank experts (2016)
  3. Optimal dynamic pricing of inventories with stochastic demand over finite horizons (1994)
  4. Dynamic pricing with limited supply (2015)
  5. The Hyperdrive Protocol: An Automated Market Maker for Fixed and Variable Rates (2024) — link
  6. Thinking fast and slow: Data-driven adaptive defi borrow-lending protocol (2024) — link
  7. AgileRate: Bringing Adaptivity and Robustness to DeFi Lending Markets (2024) — link
  8. Optimal risk-aware interest rates for decentralized lending protocols — → 2502.19862
  9. The economics of interest rate models in decentralised lending protocols (2023)
  10. Perpetual Demand Lending Pools — → 2502.06028
  11. Aave Market Risk Assessment (2021)
  12. Improving proof of stake economic security via MEV redistribution (2022)
  13. The Pricing And Hedging Of Constant Function Market Makers (2023) — link
  14. Delta hedging liquidity positions on automated market makers (2022) — link
  15. Optimal delta hedging for options (2017)
  16. Adapted hedging (2016)
  17. Staking pool centralization in proof-of-stake blockchain network (2020)
  18. Attacks on dynamic defi interest rate curves (2023) — link
  19. Equilibrium in a defi lending market (2023)
  20. An analysis of intent-based markets (2024) — link
  21. Execution Welfare Across Solver-based DEXes (2024)
  22. Logarithmic regret algorithms for online convex optimization (2007)
  23. Regret in the on-line decision problem (1999)
  24. Calibrated learning and correlated equilibrium (1997)
  25. A survey of algorithms and analysis for adaptive online learning (2017)
  26. Convex optimization (2004)
  27. Improved dynamic regret for non-degenerate functions (2017)
  28. Human-level play in the game of Diplomacy by combining language models with strategic reasoning (2022)
  29. Non-stationary stochastic optimization (2015)
  30. Online computation and competitive analysis (2005)
  31. Randomized primal-dual analysis of ranking for online bipartite matching (2013)
  32. An optimal algorithm for on-line bipartite matching (1990)
  33. Adaptive market making via online learning (2013)
  34. Market Making without Regret — → 2411.13993
  35. Competitive ratio vs regret minimization: achieving the best of both worlds (2019)
  36. Superhuman AI for multiplayer poker (2019)
  37. Dynamic regret of convex and smooth functions (2020)
  38. Online learning: A comprehensive survey (2021)
  39. The principal–agent problem in liquid staking (2023)
  40. Online convex programming and generalized infinitesimal gradient ascent (2003)
  41. Interest rate parity in decentralized finance (2023)
  42. Jupiter Perps Fees — Dune (2024)
  43. Why Traders Are Flocking to Hyperliquid (2024)
  44. gmx-io / All Stats — Dune (2024)
  45. Valuation of loan guarantees (1980)
  46. Equilibrium staking levels in a proof-of-stake blockchain (2021)
  47. Economic implications of scaling blockchains: Why the consensus protocol matters (2020)
  48. How Hard is Takeover in DPoS Blockchains? Understanding the Security of Coin-based Voting Governance. (2023)
  49. Casper the friendly finality gadget (2017) — link
  50. Leveraging Architectural Approaches in Web3 Applications-A DAO Perspective Focused (2023)
  51. Defending against malicious reorgs in Tezos Proof-of-Stake (2020)
  52. An Empirical Study on Snapshot DAO s (2022) — link
  53. Analyzing voting power in decentralized governance: Who controls DAOs ? (2022) — link
  54. Understanding Blockchain Governance: Analyzing Decentralized Voting to Amend DeFi Smart Contracts (2023) — link
  55. Understanding decentralization of decision-making power in proof-of-stake blockchains: an agent-based simulation approach (2022)
  56. Selfish behavior in the tezos proof-of-stake protocol (2021)
  57. Reward sharing schemes for stake pools (2020)
  58. Staking pools on blockchains (2022) — link
  59. Ethereum Proof-of-Stake Consensus Layer: Participation and Decentralization (2023) — link
  60. Evolution of shares in a proof-of-stake cryptocurrency (2021)
  61. Compounding of wealth in proof-of-stake cryptocurrencies (2019)
  62. Do the rich get richer? Fairness analysis for blockchain incentives (2021)
  63. Artificial Intelligence, Third Edition (1992)
  64. Power in liquid democracy (2021)
  65. Weighted voting on the blockchain: Improving consensus in proof of stake protocols (2020)
  66. Credible, Optimal Auctions via Blockchains (2023) — link
  67. Walkthrough episode 3 - Using Risk Premiums to price risk and liquidity in Aave V4 (2025) — link
  68. The newsvendor problem: Review and directions for future research (2011)
  69. Pricing and the newsvendor problem: A review with extensions (1999)
  70. Credible, Truthful, and Two-Round (Optimal) Auctions via Cryptographic Commitments (2020) — link
  71. Credible Auctions: A Trilemma (2020) — link
  72. A Theory of Auditability for Allocation and Social Choice Mechanisms (2023) — link
  73. A Theory of Auctions and Competitive Bidding (1982)
  74. Statistical Inference (2002) — link
  75. Shill-Proof Auctions (2024) — link
  76. A prior-independent revenue-maximizing auction for multiple additive bidders (2016)
  77. Multi-Item Nontruthful Auctions Achieve Good Revenue (2022)
  78. Multi-parameter mechanism design and sequential posted pricing (2010) — link
  79. Robust Restaking Networks (2024) — link
  80. EIGEN: The Universal Intersubjective Work Token (2024) — link
  81. EigenLayer: The Restaking Collective (2023) — link
  82. Gearbox Protocol Overview (2024) — link
  83. Proposal: Swapping USDT to USDC in JLP for Boosted Yield (2024) — link
  84. [Gauntlet] - Dual Slope Borrowing Rate Model Implementation and Recommendations (12/19/24) (2024) — link
  85. How much should you pay for restaking security? — → 2408.00928
  86. The collateral rule: Evidence from the credit default swap market (2022)
  87. Introducing the EigenLayer Security Model: A Novel Approach to Operating and Securing Decentralized Services (2024) — link
  88. Modeling term structures of defaultable bonds (1999)
  89. A theory of collateral requirements for central counterparties (2022)
  90. Arbitrage-free bilateral counterparty risk valuation under collateralization and application to credit default swaps (2014)
  91. Everything you always wanted to know about XVA model risk but were afraid to ask (2021) — link
  92. XVA: credit, funding and capital valuation adjustments (2015)
  93. The XVA challenge: Counterparty risk, funding, collateral, capital and initial margin (2020)
  94. Credit value adjustment for credit default swaps via the structural default model (2009)
  95. Funding value adjustments (2019)
  96. Arbitrage-Free Pricing of XVA for American Options in Discrete Time (2017)
  97. Arbitrage-free XVA (2018)
  98. Robust XVA (2020)
  99. A simple robust link between American puts and credit protection (2011)
  100. Stochastic calculus for finance I: the binomial asset pricing model (2005)
  101. Improved price oracles: Constant function market makers (2020)
  102. Replicating market makers (2023)
  103. Fundamentals of perpetual futures — → 2212.06888
  104. Perpetual futures pricing — → 2310.11771
  105. A primer on perpetuals (2023)
  106. ETF arbitrage under liquidity mismatch (2017)
  107. When does the tail wag the dog? Curvature and market making (2022)
  108. What are Mark Price and price index in USD-margined futures? (2024) — link
  109. Morpho or Euler? Comparing lending hyperstructures (2024) — link
  110. Exploring decentralized governance: a framework applied to compound finance (2023)
  111. Decentralized lending and its users: Insights from Compound (2023)
  112. Morpho (2025) — link
  113. Euler (2025) — link
  114. Euler Earn Whitepaper (2024) — link
  115. Euler - The Modular Lending Platform (2025) — link
  116. Introducing MetaMorpho: Permissionless lending vaults on Morpho Blue (2023) — link
  117. What is $JLP? (2024) — link
  118. Hedged JLP Whitepaper (2024) — link
  119. Providing Liquidity on V1 (2024) — link
  120. Providing Liquidity on V2 (2024) — link
  121. Opinion: Why DeFi liquidity providers don’t worry about impermanent loss (2024) — link
  122. GMX (2024) — link
  123. Hyperliquid HLP (2024) — link
  124. Hyperliquid Stats (2024) — link
  125. Panoptic: the perpetual, oracle-free options protocol (2022) — link
  126. Options market makers׳ hedging and informed trading: Theory and evidence (2015)
  127. Option market making under inventory risk (2009)
  128. Jupiter Summary - Risk Dashboard (2024) — link
  129. Uniswap liquidity provision: An online learning approach (2023)
  130. Strategic liquidity provision in uniswap v3 (2021) — link
  131. Adaptive Curves for Optimally Efficient Market Making — → 2406.13794
  132. Markowitz Portfolio Construction at Seventy — → 2401.05080
  133. Schur complements and statistics (1981)
  134. Schur Complementary Allocation: A Unification of Hierarchical Risk Parity and Minimum Variance Portfolios — → 2411.05807
  135. Agents’ Behavior and Interest Rate Model Optimization in DeFi Lending (2024)
  136. Building diversified portfolios that outperform out-of-sample (2016)
  137. dYdX MegaVault (2024) — link
  138. Price Impact on GMX Now Much Lower (2024) — link
  139. Unified approach for hedging impermanent loss of liquidity provision — → 2407.05146
  140. DEX to CEX Futures Trade Volume (2024) — link
  141. Protocol Vaults (2024) — link
  142. Hyperliquid HLP Vault (2024) — link
  143. Vaults (2024) — link
  144. Primer on monotone operator methods (2016)
  145. The computational power of optimization in online learning (2016)
  146. The Schur complement and its applications (2006)
  147. Risk Assessment - USDe Morpho Lending Integration (2024) — link
  148. [ARC] Gauntlet Interest Rate Curve Changes for Aave V3 Markets (Feb 2023) (2023) — link
  149. [ARFC] Aave V2 Interest Rate Curve Recommendations from Gauntlet (2023-04-21) (2023) — link
  150. What is Looping? (2023) — link
  151. Deep Dive: MegaVaault (2024) — link
  152. High-frequency trading in a limit order book (2008)
  153. FTX and Failed Custody Rules: The Collapse that Shocked the World (2023)
  154. Testimony of Hilary J. Allen, US Senate Committee on Banking, Housing, and Urban Affairs Hearing on’Crypto Crash: Why the FTX Bubble Burst and the Harm to Consumers’ (2022)
  155. A decision-theoretic generalization of on-line learning and an application to boosting (1997)
  156. Mirror descent and nonlinear projected subgradient methods for convex optimization (2003)
  157. Foundations of bilevel programming (2002)
  158. Bilevel programming problems (2015)
  159. Contagion. FTX, A Sector’s Crisis & Crypto’s Silent Victims. (2024)
  160. Constant function market makers: Multi-asset trades via convex optimization (2022)
  161. The geometry of constant function market makers — → 2308.08066
  162. Market Clearing with Semi-fungible Assets (2025)
  163. Automated market making and loss-versus-rebalancing (2022) — link
  164. An analysis of the market risk to participants in the compound protocol (2020)
  165. Adwords and generalized online matching (2007)
  166. An introduction to the theory of point processes: volume I: elementary theory and methods (2003)
  167. Essentials of stochastic processes (1999)
  168. An analysis of Uniswap markets (2021)
  169. VaultUtils.sol (2023) — link
  170. v4-chain/protocol/x/vault/genesis.go (2024) — link
  171. Asymptotically optimal competitive ratio for online allocation of reusable resources (2020) — link

11 of 179 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.