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Steven Shreve is speaking tomorrow (Tuesday 4/26) @1pm at Columbia on Optimal Execution

Optimal Execution in a General One-Sided Limit-Order Book

Date: 04-26-2011
Start Time: 1:00pm
End Time: 2:00pm
Speaker: Steven Shreve, Carnegie Mellon University
Location: Mudd 303

We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time.
Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limit-order book that determines the price. The limit-order book is permitted to have arbitrary shape. The form of the optimal execution strategy is to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency. At the end of this period, another lump purchase is made, and following that there is again a period of purchasing continuously at a rate set to match the order book resiliency. At the end of this second period, there is a final lump purchase. Any of the lump purchases could be of size zero. A simple condition is provided that guarantees that the intermediate lump purchase is of size zero.

This is joint work with Silviu Predoiu and Gennady Shaikhet. The paper has appeared in SIAM Journal on Finance Mathematics 2 (2011), 183-212.