Execute a buy/sell order on your stock with a size of X =100,000 shares within four hours with the best possible execution. You want to realize the lowest possible total execution cost B. You work with a market impact model that estimates the cost of each of n equal-sized executions, B/n, to have a fixed component F and a variable cost component , where is the number of shares traded in any given execution i:

You have estimated F to be $2, based on the order processing costs of each transaction. Market impact costs are estimated with the square root function with v equal to 0.001.

What are the optimal number of equal size transactions and what are the optimal transaction sizes?