In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread, stochastic volatility and intensities of market orders) provided the full system is Markov. The solution of the corresponding HJB equation is exact in the case of zero inventory risk. The inventory risk enters into play in two ways: a path-dependent penalty based on the volatility and a penalty at expiry based on the market spread. We perform perturbation methods on the inventory risk parameter and obtain explicitly the solution and its controls up to first order. We also include transaction costs; we show that the spread of the market-maker is widened to compensate the transaction costs, but the expected gain per traded spread remains constant. We perform several numerical simulations to assess the effect of the parameters on the PNL, showing in particular how the directional bet and the inventory risk change the shape of the PNL density. Finally, we extend our results to the case of multi-aset market-making strategies; we show that the correct notion of inventory risk is the L2-norm of the (multi-dimensional) inventory with respect to the inventory penalties.

We use data on wealth of the richest persons taken from the "rich lists" provided by business magazines like Forbes to verify if upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012 and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, usually they are also consistent with some rivals like the log-normal or stretched exponential distributions.

Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that time series data can usefully be studied as information -- by noting the relationship between statistical redundancy and dependence, we are able to use the results of information theory to construct a test for joint dependence of random variables. The test is in the same spirit of those developed by Ryabko and Astola (2005, 2006b,a), but differs from these in that we add extra randomness to the original stochatic process. It uses data compression to estimate the entropy rate of a stochastic process, which allows it to measure dependence among sets of random variables, as opposed to the existing econometric literature that uses entropy and finds itself restricted to pairwise tests of dependence. We show how serial dependence may be detected in S&P500 and PSI20 stock returns over different sample periods and frequencies. We apply the test to synthetic data to judge its ability to recover known temporal dependence structures.

It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful micro-level explanation for such fat-tailed outcomes, using agents whose private valuations have Normally-distributed errors, but whose utility function includes a term for the percentage of others who also buy.

Reputation is a key social construct in science. However, the relation between this key signaling credential and career growth remains poorly understood. Here we develop an original framework for measuring how citation paths are shaped by two distinct factors - the scientific merit of each individual paper versus the reputation of its authors within the scientific community. To estimate the relative influence of these two factors we perform a longitudinal analysis of publication data for 450 leading scientists from biology, physics, and mathematics. Our panel data approach quantifies the role of social ties, author reputation, and the citation life cycle of individual papers. We uncover statistical regularities in the coevolution of publications and citations, which we use as benchmarks to test and validate a stochastic model for the citation dynamics governing a scientists publication portfolio. We find strong evidence of increasing returns to scale in the growth of both publications and citations, reflecting the amplifying role of social processes. Moreover, our analysis shows that author reputation dominates in the initial phase of a papers citation life cycle. This latter result suggests that papers gain a significant early citation advantage if written by authors already having high reputations in the scientific community. As quantitative measures become increasingly common in the evaluation of scientific careers, our results show that the use of measures that do not account for reputation effects may paradoxically counteract the goal of sustaining talented and diligent young academics.

A large number of published studies have examined the properties of either networks of citation among scientific papers or networks of coauthorship among scientists. Here, using an extensive data set covering more than a century of physics papers published in the Physical Review, we study a hybrid coauthorship/citation network that combines the two, which we analyze to gain insight into the correlations and interactions between authorship and citation. Among other things, we investigate the extent to which individuals tend to cite themselves or their collaborators more than others, the extent to which they cite themselves or their collaborators more quickly after publication, and the extent to which they tend to return the favor of a citation from another scientist.

We stress-test the career predictability model proposed by Acuna et al. [Nature 489, 201-202 2012] by applying their model to a longitudinal career data set of 100 Assistant professors in physics, two from each of the top 50 physics departments in the US. The Acuna model claims to predict h(t+\Delta t), a scientist's h-index \Delta t years into the future, using a linear combination of 5 cumulative career measures taken at career age t. Here we investigate how the "predictability" depends on the aggregation of career data across multiple age cohorts. We confirm that the Acuna model does a respectable job of predicting h(t+\Delta t) up to roughly 6 years into the future when aggregating all age cohorts together. However, when calculated using subsets of specific age cohorts (e.g. using data for only t=3), we find that the model's predictive power significantly decreases, especially when applied to early career years. For young careers, the model does a much worse job of predicting future impact, and hence, exposes a serious limitation. The limitation is particularly concerning as early career decisions make up a significant portion, if not the majority, of cases where quantitative approaches are likely to be applied.

We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barab\'asi and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent $\beta$ as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.

Economics does not need a scientific revolution. Economics needs accurate measurements according to high standards of natural sciences and meticulous work on revealing empirical relationships between measured variables.

The current economic crisis has provoked an active response from the interdisciplinary scientific community. As a result many papers suggesting what can be improved in understanding of the complex socio-economics systems were published. Some of the most prominent papers on the topic include (Bouchaud, 2009; Farmer and Foley, 2009; Farmer et al, 2012; Helbing, 2010; Pietronero, 2008). These papers share the idea that agent-based modeling is essential for the better understanding of the complex socio-economic systems and consequently better policy making. Yet in order for an agent-based model to be useful it should also be analytically tractable, possess a macroscopic treatment (Cristelli et al, 2012). In this work we shed a new light on our research group's contributions towards understanding of the correspondence between the inter-individual interactions and collective behavior. We also provide some new insights into the implications of the global and local interactions, the leadership and the predator-prey interactions in the complex socio-economic systems.