Mean Field Limit of a Behavioral Financial Market Model

In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts of financial data. We derive the mean field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman (Physica A, 354) and show that the kinetic limit is a good approximation of the original model. Our kinetic model is able to replicate some of the most prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock price returns and volatility clustering. Interestingly, psychological misperceptions of investors can be accounted to be the origin of the appearance of stylized facts. The mesoscopic model allows us to study the model analytically. We derive steady state solutions and entropy bounds of the deterministic skeleton. These first analytical results already guide us to explanations for the complex dynamics of the model

Learn with SAT to Minimize B\"uchi Automata

We describe a minimization procedure for nondeterministic B\"uchi automata (NBA). For an automaton A another automaton A_min with the minimal number of states is learned with the help of a SAT-solver. This is done by successively computing automata A' that approximate A in the sense that they accept a given finite set of positive examples and reject a given finite set of negative examples. In the course of the procedure these example sets are successively increased. Thus, our method can be seen as an instance of a generic learning algorithm based on a "minimally adequate teacher" in the sense of Angluin. We use a SAT solver to find an NBA for given sets of positive and negative examples. We use complementation via construction of deterministic parity automata to check candidates computed in this manner for equivalence with A. Failure of equivalence yields new positive or negative examples. Our method proved successful on complete samplings of small automata and of quite some examples of bigger automata. We successfully ran the minimization on over ten thousand automata with mostly up to ten states, including the complements of all possible automata with two states and alphabet size three and discuss results and runtimes; single examples had over 100 states.Comment: In Proceedings GandALF 2012, arXiv:1210.202

Research and Development Expenditures of Innovative Enterprises in the Time of Crisis

In an analysed group of enterprises the smallest "resistance" to crisis was observed in American companies. The enterprises from the EU also reduced research and development expenditures but the pace of a fall in these expenditures was smaller than in the case of American companies.W badanej zbiorowości przedsiębiorstw najmniejszą "odporność" na kryzys wykazaly firmy amerykańskie. Firmy wywodzące się z UE również zanotowaly zmniejszenie nakladów na badania i rozwój, jednak tempo spadku nakladów badawczo-rozwojowych bylo tu mniejsze niż w przypadku firm amerykańskich

A multiple factor model for European stocks

We present an empirical study focusing on the estimation of a fundamental multi-factor model for a universe of European stocks. Following the approach of the BARRA model, we have adopted a cross-sectional methodology. The proportion of explained variance ranges from 7.3% to 66.3% in the weekly regressions with a mean of 32.9%. For the individual factors we give the percentage of the weeks when they yielded statistically significant influence on stock returns. The best explanatory power – apart from the dominant country factors – was found among the statistical constructs „success“ and „variability in markets“.Vorgestellt wird eine empirische Studie, welche die Schätzung eines fundamentalen Multi-Faktor-Modells für ein Universum europäischer Aktien beinhaltet. Als Methode wurde in Anlehnung an die Vorgehensweise im BARRA-Modell der Querschnittsanalyse der Vorzug gegeben. Der Anteil der erklärten Varianz beläuft sich in den wöchentlichen Regressionen auf 7,3% bis 66,3% bei einem Durchschnitt von 32,9%. Für die einzelnen Faktoren wird die Häufigkeit angegeben, mit der sie sich in den Regressionen signifikant erwiesen haben. Den höchsten Erklärungsgehalt im Untersuchungszeitraum hatten Länderfaktoren, aber auch Konstrukte wie „Success“ oder „Variability in Markets“

Promotion on oscillating and alternating tableaux and rotation of matchings and permutations

Using Henriques' and Kamnitzer's cactus groups, Sch\"utzenberger's promotion and evacuation operators on standard Young tableaux can be generalised in a very natural way to operators acting on highest weight words in tensor products of crystals. For the crystals corresponding to the vector representations of the symplectic groups, we show that Sundaram's map to perfect matchings intertwines promotion and rotation of the associated chord diagrams, and evacuation and reversal. We also exhibit a map with similar features for the crystals corresponding to the adjoint representations of the general linear groups. We prove these results by applying van Leeuwen's generalisation of Fomin's local rules for jeu de taquin, connected to the action of the cactus groups by Lenart, and variants of Fomin's growth diagrams for the Robinson-Schensted correspondence

Linear fractional transformations mod one and ergodic theory

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Productivity Differences in the European Union: National, Regional and Spatial Effects

Using panel data on European regions and applying Analysis of Covariance, our study provides an empirical assessment of the relative importance of national, regional and spatial factors for explaining variations of productivity. Our analysis shows that initial economic conditions or agglomeration and centrality are indeed relevant for differences in productivity levels. What is far more important, however, is which country a region belongs to. Productivity differences in the European Union are thus obviously dominated by national regimes. In light of the historically strong influence of the nation states, this result may come as no surprise. What is surprising is the fact that the role of countries has not decreased over time, despite intensive integration efforts (European Single Market, Economic and Monetary Union).Regional productivity, agglomeration and centrality, panel data econometrics