The aim of the paper is to derive for the neg 599 ative correlation function with a time parameter an asymptotic disjunction of the numerical generalized least-squares estimator of an unknown constant mean of random field in fact the correct classic generalized least-squares estimator of an unknown constant mean of the field.

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.

ac7 We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.

In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game with number of strategies for each agent S=2 and "fake" market histories. The dynamics derived is a generalized geometric Brownian motion; from the Black&Scholes formula the calibration of the Mi 660 nority Game, by means of the game parameter $ \sigma^{2}$, on the European options on DAX Index market is performed. An "$ (\alpha,\sigma^{2})$ -matrix" containing, given options' moneyness and maturities, values of the parameters $\alpha$ and $ \sigma^{2}$ that make the theoretical option price agree with the market price is constructed. We conclude that the asymmetric phase of the Minority Game with $\alpha$ close to $\alpha_c$ is coherent with options implied volatility market.

For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic 6eb investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren--Chriss model. Conditions for the absence of price manipulation for all Almgren--Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact, and the additional penalization of orders executed in the dark pool. When a particular Almgren--Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint.

We propose and document the evidence for an analogy between the dynamics of granular counter-flows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counter-flows of simulated pedestrians through a door display many stylized facts observed in financial markets when the density around the door is compared with the logarithm of the price. The stylized properties are present already when the agents in the pedestrian model are assumed to display a zero-intelligent behavior. If agents are given decision-making capacity and adapt to partially follow the majority, periods of herding behavior may additionally occur. This generates the very slow decay of the autocorrelation of absolute return due to an intermittent dynamics. Our finding suggest that the stylized facts in the fluctuations of the financial prices result from a competition of two groups with opposite interests in the presence of a constraint funneling the flow of transactions to a narrow band of prices.

How far and how fast does information spre 95e ad in social media? Researchers have recently examined a number of factors that affect information diffusion in online social networks, including: the novelty of information, users' activity levels, who they pay attention to, and how they respond to friends' recommendations. Using URLs as markers of information, we carry out a detailed study of retweeting, the primary mechanism by which information spreads on the Twitter follower graph. Our empirical study examines how users respond to an incoming stimulus, i.e., a tweet (message) from a friend, and reveals that %retweeting behavior is constrained by a few simple principles. the "principle of least effort" combined with limited attention plays a dominant role in retweeting behavior. Specifically, we observe that users retweet information when it is most visible, such as when it near the top of their Twitter stream. Moreover, our measurements quantify how a user's limited attention is divided among incoming tweets, providing novel evidence that highly connected individuals are less likely to propagate an arbitrary tweet. Our study indicates that the finite ability to process incoming information constrains social contagion, and we conclude that rapid decay of visibility is the primary barrier to information propagation online.

We 7e4 extend the formalism of Random Boolean Networks with canalizing rules to multilevel complex networks. The formalism allows to model genetic networks in which each gene might take part in more than one signaling pathway. We use a semi-annealed approach to study the stability of this class of models when coupled in a multiplex network and show that the analytical results are in good agreement with numerical simulations. Our main finding is that the multiplex structure provides a mechanism for the stabilization of the system and of chaotic regimes of individual layers. Our results help understanding why some genetic networks that are theoretically expected to operate in the chaotic regime can actually display dynamical stability.

A system of interdependent networks was recently found to be very vulnerable since cascading failures that may lead to abrupt breakdown of the system. We develop an analytical method, based on the percolation method developed for single networks [M.E.J. Newman, Phys. Rev. Lett. {\bf 103}, 058701 (2009)], to study the effect of clustering within the networks on the robustness of the interdependent networks. We find that, in contrast to single networks where the percolation threshold, $p_c$, does not change with clustering for site percolation and {\it decreases} with clustering for bond percolation, $p_c$ for interdependent networks {\it increases} when networks are more clustered.

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into ac 80b count both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the Susceptible-Infectious-Recovered model in four different real weighted networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economics perspective when compared to the unweighted method.

Data confidentiality policies at major social network providers have severely limited researchers' access to large-scale datasets. The biggest impact has been on the study of network dynamics, where researchers have studied citation graphs and content-sharing networks, but few have analyzed detailed dynamics in the massive social networks that dominate the web today. In this paper, we present results of analyzing detailed dynamics in the Renren social network, covering a period of 2 years when the network grew from 1 user to 19 million users and 199 million edges. Rather than validate a single model of network dynamics, we analyze dynamics at different granularities (user-, community- and network- wide) to determine how much, if any, users are influenced by dynamics processes at different scales. We observe in- dependent predictable processes at each level, and find that while the growth of communities has moderate and sustained impact on users, significant events such as network merge events have a strong but short-lived impact that is quickly dominated by the continuous arrival of new users.

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.

We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing to take into account possible risk underestimations due to the non-optimality of the portfolio weights being used in order to distinguish such non-optimality effects from risk underestimations genuinely due to non-stationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices.

Financial markets are well known examples of multi-fractal complex systems that have garnered much interest in their characterization through complex network theory. The recent studies have used correlation based distance metrics for defining and analyzing financial networks. In this work the singularity strength is employed to define a distance metric and the existence of hierarchical structure in the Johannesburg Stock Exchange is investigated. The multi-fractal nature of the financial market, which is otherwise hidden in the correlation coefficient based prescriptions, is analyzed through the use of the singularity strength based method. The presence of a super cluster is exhibited in the network which accounts for half of the network size and is homogeneous in the sectoral composition of the South African market.

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.

A theory of exceptional extreme events, characterized by their abnormal sizes 885 compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.

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.

We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence demonstrate the presence of a phase transition in matrix methods for community detection, such as the popular modularity maximization method. The transition separates a regime in which such methods successfully detect the community structure from one in which the structure is present but is not detected. By comparing these results with recent analyses of maximum-likelihood methods we are able to show that spectral modularity maximization is an optimal detection method in the sense that no other method will succeed in the regime where the modularity method fails.

The existence of imitative behavior among consumers is a well-known phenomenon in the field of Economics. This behavior is especially common in markets determined by a high degree of innovation, asymmetric information and/or price-inelastic demand, features that exist in the pharmaceutical market. This paper presents evidence of the existence of imitative behavior among primary care physicians in Galicia (Spain) when choosing treatments for their patients. From this and other evidence, we propose a dynamic model for determining the entry of new drugs into the market. To do this, we introduce the structure of the organization of primary health care centers and the presence of groups of doctors who are specially interrelated, as well as the existence of commercial pressure on doctors. For modeling purposes, physicians are treated as spins connected in an exponentially distributed complex network of the Watts-Strogatz type. The proposed model provides an explanation for the differences observed in the patterns of the introduction of technological innovations in different regions. The main cause of these differences is the different structure of relationships among consumers, where the existence of small groups that show a higher degree of coordination over the average is particularly influential. The evidence presented, together with the proposed model, might be useful for the design of optimal strategies for the introduction of new drugs, as well as for planning policies to manage pharmaceutical expenditure.

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST-symmetry is spontaneously broken by instantons, which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent modulii of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is "self-tuned". The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some of SOC's and the concept of topological quantum computing.