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on History and Philosophy of Economics |
| By: | Carlos Pedro Gon\c{c}alves |
| Abstract: | A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure exchange economies and the finite-state securities market optimization problem, thus addressing, within the financial setting, the interplay between companies' business games and financial agents' behavior. A complete set of quantum Arrow-Debreu prices, resulting from the game of strategy's quantum Nash equilibrium, is shown to hold, even in the absence of securities' market completeness, such that Pareto optimal results are obtained without having to assume the completeness condition that the rank of the securities' payoff matrix is equal to the number of alternative lottery states. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.2080&r=hpe |
| By: | Neil Johnson; Guannan Zhao; Eric Hunsader; Jing Meng; Amith Ravindar; Spencer Carran; Brian Tivnan |
| Abstract: | Society's drive toward ever faster socio-technical systems, means that there is an urgent need to understand the threat from 'black swan' extreme events that might emerge. On 6 May 2010, it took just five minutes for a spontaneous mix of human and machine interactions in the global trading cyberspace to generate an unprecedented system-wide Flash Crash. However, little is known about what lies ahead in the crucial sub-second regime where humans become unable to respond or intervene sufficiently quickly. Here we analyze a set of 18,520 ultrafast black swan events that we have uncovered in stock-price movements between 2006 and 2011. We provide empirical evidence for, and an accompanying theory of, an abrupt system-wide transition from a mixed human-machine phase to a new all-machine phase characterized by frequent black swan events with ultrafast durations (<650ms for crashes, <950ms for spikes). Our theory quantifies the systemic fluctuations in these two distinct phases in terms of the diversity of the system's internal ecology and the amount of global information being processed. Our finding that the ten most susceptible entities are major international banks, hints at a hidden relationship between these ultrafast 'fractures' and the slow 'breaking' of the global financial system post-2006. More generally, our work provides tools to help predict and mitigate the systemic risk developing in any complex socio-technical system that attempts to operate at, or beyond, the limits of human response times. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1448&r=hpe |
| By: | Michael C. M\"unnix; Takashi Shimada; Rudi Sch\"afer; Francois Leyvraz Thomas H. Seligman; Thomas Guhr; H. E. Stanley |
| Abstract: | The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1623&r=hpe |
| By: | Jo\~ao P. da Cruz; Pedro G. Lind |
| Abstract: | The study of heavy-tailed distributions in economic and financial systems has been widely addressed since financial time series has become a research subject.After the eighties, several "highly improbable" market drops were observed (e.g. the 1987 stock market drop known as "Black Monday" and on even more recent ones, already in the 21st century) that produce heavy losses that were unexplainable in a GN environment. The losses incurred in these large market drop events did not change significantly the market practices or the way regulation is done but drove some attention back to the study of heavy-tails and their underlying mechanisms. Some recent findings in these context is the scope of this manuscript. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.0142&r=hpe |