Executing large orders in a microscopic market model

In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple order book based model for the impact of large orders on stock prices. They use this model to derive optimal strategies for the execution of large orders. We apply these strategies to an agent-based stochastic order book model that was recently proposed by Bovier, \v{C}ern\'{y} and Hryniv, but already the calibration fails. In particular, from our simulations the recovery speed of the market after a large order is clearly dependent on the order size, whereas the AFS model assumes a constant speed. For this reason, we propose a generalization of the AFS model, the GAFS model, that incorporates this dependency, and prove the optimal investment strategies. As a corollary, we find that we can derive the ``correct'' constant resilience speed for the AFS model from the GAFS model such that the optimal strategies of the AFS and the GAFS model coincide. Finally, we show that the costs of applying the optimal strategies of the GAFS model to the artificial market environment still differ significantly from the model predictions, indicating that even the improved model does not capture all of the relevant details of a real market.Comment: 32 pages, 12 figure

On Shephard Groups with Large Triangles

Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form small cancellation theory we show that the groups in this family are bi-automatic.Comment: 30 pages, 11 PDF figure

Battery powered high efficiency drive systems in practical applications

Since about 30 years three-phase variable speed drives are the standard industrial solution when high reliability, high ingress protection of machine and especially high efficiency are required. Generally, these drives are powered from the grid due to their high power capability. Through Lithium-Ion rechargable batteries, electric variable speed drives for commercial vehicles as cars and trucks become feasible. These Lithium-Ion batteries are no more a completely constant voltage source but vary the voltage mainly dependent on state of charge by about plus and minus 15%. Power electronics for the drive have to cope with this and are strongly influenced by the type of motor, too. Power insertion comes from the grid by special chargers or in case of big mining trucks, by catenaries. Commercial battery powered drives are common between some kW up to 100 kW but are extended up to 800 kW in a heavy truck implementation study