Flash Loan Arbitrage Documentation Table of Contents Introduction Identifying Ideal Pools Calculating Optimal Amount to Swap Calculating Expected Profit Introduction This documentation outlines the mathematical approach for leveraging flash loans for price manipulation and arbitrage opportunities in Uniswap V2 pools.

Identifying Ideal Pools Slippage Threshold Liquidity of the Pool: L_pool Amount of Token A to be borrowed: Δx Resulting change in Token B after swap: Δy Slippage Formula: Price Impact = Δy / (x + Δx) Slippage Threshold: Price Impact Threshold = Δx / (x + Δx) > ε (e.g., 1% or 5%) Pseudocode def calculate_slippage_threshold(L_pool, Δx, x): Δy = calculate_Δy(L_pool, Δx, x) price_impact = Δy / (x + Δx) return price_impact > ε

Calculating Optimal Amount to Swap Profit Function Arbitrage Price Difference: P_target - P_manipulated Amount of Arbitraged Token: Δx Flash Loan Fee: f_loan * Δx Gas Fees: G Profit Function: Profit = (Arbitrage Price Difference) * (Amount of Arbitraged Token) - Flash Loan Fee - Gas Fees Pseudocode def calculate_optimal_amount_to_swap(L_pool, Δx, x, P_target, P_manipulated, f_loan, G): arbitrage_price_difference = P_target - P_manipulated profit = (arbitrage_price_difference * Δx) - (f_loan * Δx) - G return Δx

Calculating Expected Profit Price Shift Due to Flash Loan New Price of Token B: (y + Δy) / (x - Δx) Arbitrage Profit: (New Price of Token B from Arbitrage Pool - Price in Target Pool) * Amount of Token B Pseudocode def calculate_expected_profit(L_pool, Δx, x, y, Δy, P_target, P_manipulated): new_price_token_b = (y + Δy) / (x - Δx) arbitrage_profit = (new_price_token_b - P_target) * Δy return arbitrage_profit

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