We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Percentage of Volume, PVol) for both TC and IS. We also study an alternative set of risk measures for the optimisation of algorithmic trading curves. We assume a self-similar process (e.g. L\'evy process, fractional Brownian motion or fractal process) and define a new risk measure, the $p$-variation, which reduces to the variance if the process is a Brownian motion. We deduce the explicit formula for the TC and IS algorithms under a self-similar process. We show that there is an equivalence between self-similar models and a family of risk measures called $p$-variations: assuming a self-similar process and calibrating empirically the parameter $p$ for the $p$-variation yields the same result as assuming a Brownian motion and using the $p$-variation as risk measure instead of the variance. We also show that $p$ can be seen as a measure of the aggressiveness: $p$ increases if and only if the TC algorithm starts later and executes faster. From the explicit expression of the TC algorithm one can compute the sensitivities of the curve with respect to the parameters up to any order. As an example, we compute the first order sensitivity with respect to both a local and a global surge of volatility. Finally, we show how the parameter $p$ of the $p$-variation can be implied from the optimal starting time of TC, and that under this framework $p$ can be viewed as a measure of the joint impact of market impact (i.e. liquidity) and volatility.

Recently, many studies indicated that the minimum spanning tree (MST) network whose metric distance is de?ned b 979 y using correlation coe?cients have strong implications on extracting infor- mation from return time series. However in many cases researchers may hope to investigate the strength of interactions but not the directions of them. In order to study the strength of interaction and connection of ?nancial asset returns we propose a modi?ed minimum spanning tree network whose metric distance is de?ned from absolute cross-correlation coe?cients. We had investigated 69 daily ?nancial time series, which constituted by 3 types ?nance assets (29 stock market indica- tor time series, 21 currency futures price time series and 19 commodity futures price time series). Empirical analyses show that the MST network of returns is time-dependent in overall structure, while same type ?nancial assets usually keep stable inter-connections. Moreover each asset in same group show similar economic characters. In other words, each group concerned with one kind of traditional ?nancial commodity. In addition, we ?nd the time-lag between stock market indicator volatility time series and EUA (EU allowances), WTI (West Texas Intermediate) volatility time series. The peak of cross-correlation function of volatility time series between EUA (or WTI) and stock market indicators show a signi?cant time shift (> 20days) from 0.

We analyze a controlled price formation experiment in the laboratory that shows evidence for bubbles. We calibrate two models that demonstrate with high statistical significance that these laboratory bubbles have a tendency to grow faster than exponential due to positive feedback. We show that the positive feedback operates by traders continuously upgrading their over-optimistic expectations of future returns based on past prices rather than on realized returns.

Predicting X from Twitter is a popular fad within the Twitter research subculture. It seems both appealing and relatively easy. Among such kind of studies, electoral prediction is maybe the most attractive, and at this moment there is a growing body of literature on such a topic. This is not only an interesting research problem but, above all, it is extremely difficult. However, most of the authors seem to be more interested in claiming positive results than in providing sound and reproducible methods. It is also especially worrisome that many recent papers seem to only acknowledge those studies supporting the idea of Twitter predicting elections, instead of conducting a balanced literature review showing both sides of the matter. After reading many of such papers I have decided to write such a survey myself. Hence, in this paper, every study relevant to the matter of electoral prediction using social media is commented. From this review it can be concluded that the predictive power of Twitter regarding elections has been greatly exaggerated, and that hard research problems still lie ahead.

The timing patterns of human communication in social networks is not random. On the contrary, communication is dominated by emergent statistical laws such as non-trivial correlations and clustering. Recently, we found long-term correlations in the user's activity in social communities. Here, we extend this work to study collective behavior of the whole community. The goal is to understand the origin of clustering and long-term persistence. At the individual level, we find that the correlations in activity are a byproduct of the clustering expressed in the power-law distribution of inter-event times of single users. On the contrary, the activity of the whole community presents long-term correlations that are a true emergent property of the system, i.e. they are not related to the distribution of inter-event times. This result suggests the existence of collective behavior, possible arising from nontrivial communication patterns through the embedding social network.