Any trading strategy is ultimately implemented by a stream of buy or sell orders. These orders are placed at trading venues whose liquidity varies over time, depending on the total flow of incoming orders. As a result, transactions affect market prices, typically in an adverse way. It thus becomes an issue how to optimally schedule the placement of single limit order market orders so as to trade-off their urgency against their costs, a challenging stochastic optimization problem to which Berlin researchers have contributed in a number of publications.
Alfonsi et al. (2010) show how to account for general limit order book shapes when liquidating a portfolio in a model with market resilience as in Obizhaeva and Wang (2005). This is complemented by Fruth (2011) who analyzes the effects of time-varying liquidity and provides a suitable numerical optimization scheme. The Optimal curve-following strategies (e.g. trading at VWAP) in illiquid markets when investors can submit active orders to traditional exchanges and simultaneously in a dark pool have been analyzed by Naujokat and Westray (2010). An extension allowing for discrete market orders and adverse selection effects in dark pools has been studied by Naujokat and Horst (2011).
- Aurelien Alfonsi, Antje Fruth, Alexander Schied, Optimal execution strategies in limit order books with general shape functions, Quantitative Finance, Vol. 10, 143-157, 2010
- Antje Fruth, Optimal Order Execution with Stochastic Liquidty, Ph.D. thesis, TU Berlin, 2011
- Felix Naujokat, Stochastic Control in Limit Order Markets, Ph.D. thesis, HU Berlin, 2011
- Felix Naujokat, Ulrich Horst, When to cross the spread: curve following with singular control, Preprint, 2011
- Felix Naujokat, Nick Westray, Curve Following in Illiquid Markets, Mathematics and Financial Economics, Vol. 4, No. 4, 299-335, 2011