Optimal liquidation in dark pools in discrete and continuous time [Elektronische Ressource] / Peter Kratz. Gutachter: Ulrich Horst ; Stefan Ankirchner ; Darrell Duffie ; Ivar Ekeland

Optimal liquidation in dark pools in discrete andcontinuous timeD I SS E R TAT I O Nzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonDipl.-Math. Peter Kratzgeboren am 8. Juli 1980 in UlmPräsident der Humboldt-Universität zu Berlin:Prof. Dr. Jan-Hendrik OlbertzDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Elmar KulkeGutachter:1. Prof. Dr. Ulrich Horst2. Prof. Dr. Stefan Ankirchner3. Prof. Dr. Darrell Duffie4. Prof. Dr. Ivar Ekelandeingereicht am: 12. Februar 2011Tag der Verteidigung: 12. Juli 2011AbstractIn recent years there has been an increasing interest in financial market modelsthat account for the impact of large transactions on asset prices. In this thesis weconsider an “illiquid market” with a risk-averse investor who has to liquidate a largeportfolio within a finite time horizon [0,T ]. At any point in time, the investor hasthe option to trade at a traditional exchange (the “primary venue”) which yieldsprice impact and to place orders in a so-called dark pool.The liquidity in dark pools is not openly displayed and dark pools do not con-tribute to the price formation process. Instead, orders are executed at the price ofthe primary venue if matching liquidity is available. Therefore, these orders have noprice impact.