Academic Paper
May 2025
Loss-Versus-Rebalancing Under Deterministic and Generalized Block-Times
Alex Nezlobin, Martin Tassy
This paper extends LVR analysis to modern proof-of-stake blockchains with deterministic block times. Using advanced random walk theory, we derive closed-form approximations for LVR under constant block intervals and prove that deterministic timing provides optimal protection against arbitrage for liquidity providers.
Key Contributions:
- First analytical formula for LVR under deterministic block times: ARB ≈ σ²ᵦ/2 + 1.7164 γ/σᵦ
- Proves constant block spacing minimizes LVR by up to 17.4% compared to Poisson timing
- Establishes universal arbitrage probability limits across all block-time distributions
- Develops discrete-time Markov chain framework using random walk theory on strips
- Provides exponentially accurate approximations validated by large-scale Monte Carlo simulations
Technical Analysis
2022
Growth Rate of a Liquidity Provider's Wealth in XY = c Automated Market Makers
Martin Tassy, David White
We analyze the geometric return of liquidity providers in constant product automated market makers under a no-arbitrage assumption. This work provides explicit formulas for LP wealth growth rates and identifies optimal fee structures for different market conditions.
Key Findings:
- Derives closed-form expressions for LP wealth growth rates with trading fees
- Identifies optimal pool weights for different asset volatility scenarios
- Establishes conditions where LP positions outperform hold strategies
- Provides convergence analysis to geometric Brownian motion models
- Offers practical insights for fee optimization and liquidity provision
