Using entropy-based local weighting to improve similarity assessment

This paper enhances and analyses the power of local weighted similarity measures. The paper proposes a new entropy-based local weighting algorithm to be used in similarity assessment to improve the performance of the CBR retrieval task. It has been carried out a comparative analysis of the performance of unweighted similarity measures, global weighted similarity measures, and local weighting similarity measures. The testing has been done using several similarity measures, and some data sets from the UCI Machine Learning Database Repository and other environmental databases.Postprint (published version

Impact of the tick-size on financial returns and correlations

We demonstrate that the lowest possible price change (tick-size) has a large impact on the structure of financial return distributions. It induces a microstructure as well as it can alter the tail behavior. On small return intervals, the tick-size can distort the calculation of correlations. This especially occurs on small return intervals and thus contributes to the decay of the correlation coefficient towards smaller return intervals (Epps effect). We study this behavior within a model and identify the effect in market data. Furthermore, we present a method to compensate this purely statistical error.Comment: 18 pages, 10 figure

Numerical methods for an optimal order execution problem

This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP) equation is a quasi-variational inequality (QVI) with solvency constraint satisfied by the value function in the sense of constrained viscosity solutions. By taking advantage of the lag variable tracking the time interval between trades, we can provide an explicit backward numerical scheme for the time discretization of the DPQVI. The convergence of this discrete-time scheme is shown by viscosity solutions arguments. An optimal quantization method is used for computing the (conditional) expectations arising in this scheme. Numerical results are presented by examining the behaviour of optimal liquidation strategies, and comparative performance analysis with respect to some benchmark execution strategies. We also illustrate our optimal liquidation algorithm on real data, and observe various interesting patterns of order execution strategies. Finally, we provide some numerical tests of sensitivity with respect to the bid/ask spread and market impact parameters