# Arbitrage optimal size model that accounts for slippage given a specific path?

I'm interested in any model that helps calculating the optimal size to maximize PnL given the liquidity of an asset (or the slippage that I would incurr per unit of asset traded).

For instance, let's say that I'm arbing between 3 products A, B and C. At time T I know the liquidity and prices (order book) of the 3 of them, but there are no opportunities. At time T+1, an update on the order book of C comes in. Is there any model that serves as a plug-and-play formula where I'd just put the updated data from C and get the quantity that would maximize the PnL in this triangle?

Of course for 1 specific path sounds easy as it's just basic algebra to calculate this optimal size, but how to do it when you have 100 assets and the path on T+1 could be any combination?

If you know of any similar models but are not sure if it would help here, please share it anyway!

Thanks!

• It's a linear programming exercise, no? Pick a solver and you're set. May 15 at 16:14
• Not sure but I think this one of the graph problems discussed elsewhere on this site. May 15 at 21:01