Optimal Flash Loan Fee Function with Respect to Leverage Strategies

We investigate two decentralized methods for leveraging assets: Firstly, investors recurrently commit their target assets as collateral to secure loans, subsequently reinvesting the borrowed funds in the same assets. Secondly, investors pledge their assets once but are required to promptly borrow from a lender and repay the borrowed amount. This model is exemplified by recent Ethereum investment strategies, where investors must weigh the trade-off between gas fees associated with multiple pledging processes and fees charged by the lender, known as the Flash Loan project. Our comprehensive analysis encompasses game theory dynamics, determining optimal strategies for self-interested investors and deriving a unique nonlinear optimal fee structure for Flash Loans. This structure remains incentive-compatible, guarding against Sybil attacks and other deviations. Empirical results, under varying environmental parameters, consistently demonstrate the superior revenue performance of our optimal fee structure compared to the commonly used linear fee model within the Flash Loan project.