Department of Mathematics

Dipl.-Math. Peter Frentrup, Humboldt-Universität Berlin: "How is optimal execution affected by price trends?"

May 16, 2019 from 10:15 AM to 11:45 AM

LMS 4 - Raum 325 - Seminarhörsaal


A large investor seeks to liquidate a financial asset position in finite time while she anticipates a general drift of market prices, which can be upwards or downwards. Depending on her initial market impact, the optimal liquidation strategy comprises an initial block buy or sale, followed by continuous selling and/or buying -- possibly entering a short position -- and finally leaving the market with a final block buy or sale to clear her position. Due to the non-zero drift, solution methods based on convex analysis are out of reach. We solve this optimal liquidation problem in two steps. Classical calculus of variations provides a candidate for the free boundary surface that separates buy and sell regions and moreover yields local optimality near said boundary. Using this local optimality result, we can extend the variational inequality to the whole state space and thereby get global optimality.



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