A Dynamical Thermostat Approach To Financial Asset Price Dynamics

A dynamical price formation model for financial assets is presented. It aims to capture the essence of speculative trading where mispricings of assets are used to make profits. It is shown that together with the incorporation of the concept of risk aversion of agents the model is able to reproduce several key characteristics of financial price series. The approach is contrasted to the conventional view of price formation in financial economics.Comment: contribution to the 6th Granada Seminar 2000: Modeling Complex Systems, 10 pages, eps figure

Nonextensive statistical mechanics and complex scale-free networks

One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather than on microscopic details of interactions of its elements. This viewpoint allows to naturally treat collective phenomena which are often an integral part of complex systems, such as biological or socio-economical phenomena. Much of the attraction of network theory arises from the discovery that many networks, natural or man-made, seem to exhibit some sort of universality, meaning that most of them belong to one of three classes: {\it random}, {\it scale-free} and {\it small-world} networks. Maybe most important however for the physics community is, that due to its conceptually intuitive nature, network theory seems to be within reach of a full and coherent understanding from first principles ..

Elimination of systemic risk in financial networks by means of a systemic risk transaction tax

Financial markets are exposed to systemic risk (SR), the risk that a major fraction of the system ceases to function, and collapses. It has recently become possible to quantify SR in terms of underlying financial networks where nodes represent financial institutions, and links capture the size and maturity of assets (loans), liabilities, and other obligations, such as derivatives. We demonstrate that it is possible to quantify the share of SR that individual liabilities within a financial network contribute to the overall SR. We use empirical data of nationwide interbank liabilities to show that the marginal contribution to overall SR of liabilities for a given size varies by a factor of a thousand. We propose a tax on individual transactions that is proportional to their marginal contribution to overall SR. If a transaction does not increase SR it is tax-free. With an agent-based model (CRISIS macro-financial model) we demonstrate that the proposed "Systemic Risk Tax" (SRT) leads to a self-organised restructuring of financial networks that are practically free of SR. The SRT can be seen as an insurance for the public against costs arising from cascading failure. ABM predictions are shown to be in remarkable agreement with the empirical data and can be used to understand the relation of credit risk and SR.Comment: 18 pages, 7 figure

Hierarchical and mixing properties of static complex networks emerging from the fluctuating classical random graphs

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.Comment: 15 pages and 3 figure

DebtRank-transparency: Controlling systemic risk in financial networks

Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is available to Central Banks. With a simple agent based model we show that by increasing transparency by making the DebtRank of individual nodes (banks) visible to all nodes, and by imposing a simple incentive scheme, that reduces interbank borrowing from systemically risky nodes, the systemic risk in the financial network can be drastically reduced. This incentive scheme is an effective regulation mechanism, that does not reduce the efficiency of the financial network, but fosters a more homogeneous distribution of risk within the system in a self-organized critical way. We show that the reduction of systemic risk is to a large extent due to the massive reduction of cascading failures in the transparent system. An implementation of this minimal regulation scheme in real financial networks should be feasible from a technical point of view.Comment: 8 pages, 5 figure

Generalized (c,d)-entropy and aging random walks

Complex systems are often inherently non-ergodic and non-Markovian for which Shannon entropy loses its applicability. In particular accelerating, path-dependent, and aging random walks offer an intuitive picture for these non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon-Khinchin axioms, and by violating the fourth -- the so-called composition axiom. The corresponding entropy is of the form $S_{c,d} \sim \sum_i \Gamma(1+d,1-c\ln p_i)$ and depends on two system-specific scaling exponents, $c$ and $d$. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work we generalize these walks to a much wider class of stochastic systems that can be characterized as `aging' systems. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks $S_{c,d}$ is again the correct extensive entropy. Before the central part of the paper we review the concept of $(c,d)$-entropy in a self-contained way.Comment: 8 pages, 5 eps figures. arXiv admin note: substantial text overlap with arXiv:1104.207