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2
votes
Ola Løvsletten, Martin Rypdal
posted by Matúš Medo (29 February 2012)
We introduce tools for inference in the multifractal random walk introduced
by Bacry et al. (2001). These tools include formulas for smoothing, filtering
and volatility forecasting. In addition, we present methods for computing
conditional densities for one- and multi-step returns. The inference techniques
presented in this paper, including maximum likelihood estimation, are applied
to data from the Oslo Stock Exchange, and it is observed that the volatility
forecasts bas
4ed
ed on the multifractal random walk have a much richer structure
than the forecasts obtained from a basic stochastic volatility model.
2
votes
V.I. Yukalov, D. Sornette
posted by Matúš Medo (29 February 2012)
Decision making of agents who are members of a society is analyzed from the
point of view of quantum decision theory. This generalizes the approach,
developed earlier by the authors for separate individuals, to decision making
under the influence of social interactions. The generalized approach not only
avoids pa
5c1
radoxes, typical of classical decision making based on utility theory,
but also explains the error-attenuation effects observed for the paradoxes
occurring when decision makers, who are members of a society, consult with each
other increasing in this way the available mutual information.
2
votes
Daniele Marinazzo, Mario Pellicoro, Guorong Wu, Leonardo Angelini, Sebastiano Stramaglia
posted by Matúš Medo (29 February 2012)
We analyze a simple dynamical network model which describes the limited
capacity of nodes to process the input information. For a suitable choice of
the parameters, the information flow pattern is characterized by exponential
distribution of the incoming information and a fat-tailed distribution of the
outgoing information, as a signature of the law of diminishing marginal
returns. The analysis of a real EEG data-set shows that similar phenomena may
be relevant for brain signals.
2
votes
Christian Borgs, Michael Brautbar, Jennifer Chayes, Sanjeev Khanna, Brendan Lucier
posted by Matúš Medo (29 February 2012)
We study the power of \textit{local information algorithms} for optimization
problems on social networks. We focus on sequential algorithms for which the
network topology is initially unknown and is revealed only within a local
neighborhood of vertices that have been irrevocably added to the output set.
The distinguishing feature of this setting is that locality is necessitated by
constraints on the network information visible to the algorithm, rather than
being desirable for reasons of efficiency or parallelizability. In this sense,
changes to the level of network visibility can have a significant impact on
algorithm design.
<br />We study a range of problems under this model of algorithms with local
information. We first consider the case in which the underlying graph is a
preferential attachment network. We show that one can find the node of maximum
degree in the network in a polylogarithmic number of steps, using an
opportunistic algorithm that repeatedly queries the visible node of maximum
degree. This addresses an open question of Bollob{\'a}s and Riordan. In
contrast, local information algorithms require a linear number of queries to
solve the problem on arbitrary networks.
<br />Motivated by problems faced by recruiters in online networks, we also
consider network coverage problems such as finding a minimum dominating set.
For this optimization problem we show that, if each node added to the output
set reveals sufficient information about the set's neighborhood, then it is
possible to design randomized algorithms for general networks that nearly match
the best approximations possible even with full access to the graph structure.
We show that this level of visibility is necessary.
<br />We conclude that a network provider's decision of how much structure to make
visible to its users can have a significant effect on a user's ability to
interact strategically with the network.
2
votes
Lazaros K. Gallos, Pablo Barttfeld, Shlomo Havlin, Mariano Sigman, Hernán A. Makse
posted by Matúš Medo (29 February 2012)
Non-communicable diseases like diabetes, obesity and certain forms of cancer
have been increasing in many countries at alarming levels. A difficulty in the
conception of policies to reverse these trends is the identification of the
drivers behind the global epidemics. Here, we implement a spatial spreading
analysis to investigate whether diabetes, obesity and cancer show spatial
correlations revealing the effect of collective and global factors acting above
individual choices. We adapt a theoretical framework for critical physical
systems displaying collective behavior to decipher the laws of spatial
spreading of diseases. We find a regularity in the spatial fluctuations of
their prevalence revealed by a pattern of scale-free long-range correlations.
The fluctuations are anomalous, deviating in a fundamental way from the weaker
correlations found in the underlying population distribution. This collective
behavior indicates that the spreading dynamics of obesity, diabetes and some
forms of cancer like lung cancer are analogous to a critical point of
fluctuations, just as a physical system in a second-order phase transition.
According to this notion, individual interactions and habits may have
negligible influence in shaping the global patterns of spreading. Thus, obesity
turns out to be a global problem where local details are of little importance.
Interestingly, we find the same critical fluctuations in obesity and diabetes,
and in the activities of economic sectors associated with food production such
as supermarkets, food and beverage stores--- which cluster in a different
universality class than other generic sectors of the economy. These results
motivate future interventions to investigate the causality of this relation
providing guidance for the implementation of preventive health policies.
2
votes
Eric Kemp-Benedict
posted by Eric Kemp-Benedict (29 February 2012)
The notion that economies should normally be in equilibrium is by now
well-established; equally well-established is that economies are almost never
precisely in equilibrium. Using a very general formulation, we sh
632
ow that under
dynamics that are second-order in time a price system can remain away from
equilibrium with permanent and repeating opportunities for arbitrage, even when
a damping term drives the system towards equilibrium. We also argue that
second-order dynamic equations emerge naturally when there are heterogeneous
economic actors, some behaving as active and knowledgeable arbitrageurs, and
others using heuristics. The essential mechanism is that active arbitrageurs
are able to repeatedly benefit from the suboptimal heuristics that govern most
economic behavior.
2
votes
Enrico Scalas, Mauro Politi
posted by Matúš Medo (22 February 2012)
A stochastic model for pure-jump diffusion (the compound renewal process) can
be used as a zero-order approximation and as a phenomenological description of
tick-by-tick price fluctuations. This leads to an exact and explicit gener
645
al
formula for the martingale price of a European call option. A complete
derivation of this result is presented by means of elementary probabilistic
tools.
1
vote
Massimo Riccaboni, Alessandro Rossi, Stefano Schiavo
posted by Matúš Medo (22 February 2012)
Considerable efforts have been made in recent years to produce detailed
topologies of the Internet. Although Internet topology data have been brought
to the attention of a wide and somewhat diverse audience of scholars, so far
they have been overlooked by economists. In this paper, we suggest that such
data could be effectively treated as a proxy to characterize the size of the
"digital economy" at country level and outsourcing: thus, we analyse the
topological structure of the network of trade in digital services (trade in
bits) and compare it with that of the more traditional flow of manufactured
goods across countries. To perform meaningful comparisons across networks with
different characteristics, we define a stochastic benchmark for the number of
connections among each country-pair, based on hypergeometric distribution.
Original data are thus filtered by means of different thresholds, so that we
only focus on the strongest links, i.e., statistically significant links. We
find that trade in bits displays a sparser and less hierarchical network
structure, which is more similar to trade in high-skill manufactured goods than
total trade. Lastly, distance plays a more prominent role in shaping the
network of international trade in physical goods than trade in digital
services.
1
vote
Nicola Bellomo, Miguel A. Herrero, Andrea Tosin
posted by Matúš Medo (22 February 2012)
This paper deals with the modeling of social competition, possibly resulting
in the onset of extreme conflicts. More precisely, we discuss models describing
the interplay between individual competition for wealth distribution that, when
coupled with political stances coming from support or opposition to a
government, may give rise to strongly self-enhanced effects. The latter may be
thought of as the early stages of massive, unpredictable events known as Black
Swans, although no analysis of any fully-developed Black Swan is provided here.
Our approach makes use of the framework of the kinetic theory for active
particles, where nonlinear interactions among subjects are modeled according to
game-theoretical tools.
1
vote
Sebastian Heise, and Reimer Kuehn
posted by Matúš Medo (20 February 2012)
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a de
89d
cade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.
1
vote
Aleksejus Kononovicius, Vygintas Gontis, Valentas Daniunas
posted by Matúš Medo (20 February 2012)
We present examples of agent-based and stochastic models of competition and
business processes in economics and finance. We start from as simple as
possible models, which have microscopic, agent-based, versions and macroscopic
treatment in behavior. Microscopic and macroscopic versions of herding model
proposed by Kirman and Bass diffusion of new products are considered in this
contribution as two basic ideas. Further we demonstrate that general herding
behavior can be considered as a background of nonlinear stochastic model of
financial fluctuations.
1
vote
A. Saichev, D. Sornette
posted by Matúš Medo (20 February 2012)
We present a simple microstructure model of financial returns that combines
(i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the
bid-ask bounce effect, (iii) the fat tail structure of the distribution of
returns and (iv) the non-Poissonian statistics of inter-trade intervals. This
model allows us to explain both qualitatively and quantitatively important
stylized facts observed in the statistics of microstructure returns, including
the short-ranged correlation of returns, the long-ranged correlations of
absolute returns, the microstructure noise and Epps effects. According to the
microstructure noise effect, volatility is a decreasing function of the time
scale used to estimate it. Paradoxically, the Epps effect states that cross
correlations between asset returns are increasing functions of the time scale
at which the returns are estimated. The microstructure noise is explained as
the result of the negative return correlations inherent in the definition of
the bid-ask bounce component (ii). In the presence of a genuine correlation
between the returns of two assets, the Epps effect is due to an average
statistical overlap of the momentum of the returns of the two assets defined
over a finite time scale in the presence of the long memory process (i).
2
votes
Linyuan Lu, Zi-Ke Zhang, Tao Zhou
posted by Matúš Medo (20 February 2012)
Zipf's law on word frequency is observed in English, French, Spanish,
Italian, and so on, yet it does not hold for Chinese, Japanese or Korean
characters. A model for writing process is proposed to explain the above
difference, which takes into account the ef
73f
fects of finite vocabulary size.
Experiments, simulations and analytical solution agree well with each other.
The results show that the frequency distribution follows a power law with
exponent being equal to 1, at which the corresponding Zipf's exponent diverges.
Actually, the distribution obeys exponential form in the Zipf's plot. Deviating
from the Heaps' law, the number of distinct words grows with the text length in
three stages: It grows linearly in the beginning, then turns to a logarithmical
form, and eventually saturates. This work refines previous understanding about
Zipf's law and Heaps' law in language systems.
1
vote
Márton Karsai, Kimmo Kaski, János Kertész
posted by Matúš Medo (20 February 2012)
We investigate the communication sequences of millions of people through two
different channels and analyze the fine grained temporal structure of
857
correlated event trains induced by single individuals. By focusing on
correlations between the heterogeneous dynamics and the topology of egocentric
networks we find that the bursty trains usually evolve for pairs of individuals
rather than for the ego and his/her several neighbors thus burstiness is a
property of the links rather than of the nodes. We compare the directional
balance of calls and short messages within bursty trains to the average on the
actual link and show that for the trains of voice calls the imbalance is
significantly enhanced, while for short messages the balance within the trains
increases. These effects can be partly traced back to the technological
constrains (for short messages) and partly to the human behavioral features
(voice calls). We define a model that is able to reproduce the empirical
results and may help us to understand better the mechanisms driving technology
mediated human communication dynamics.
1
vote
Ryohei Hisano, Didier Sornette
posted by Matúš Medo (20 February 2012)
What is the productivity of Science? Can we measure an evolution of the
production of mathematicians over history? Can we predict the waiting
a0d
time till
the proof of a challenging conjecture such as the P-versus-NP problem?
Motivated by these questions, we revisit a suggestion published recently and
debated in the "New Scientist" that the historical distribution of
time-to-proof's, i.e., of waiting times between formulation of a mathematical
conjecture and its proof, can be quantified and gives meaningful insights in
the future development of still open conjectures. We find however evidence that
the mathematical process of creation is too much non-stationary, with too
little data and constraints, to allow for a meaningful conclusion. In
particular, the approximate unsteady exponential growth of human population,
and arguably that of mathematicians, essentially hides the true distribution.
Another issue is the incompleteness of the dataset available. In conclusion we
cannot really reject the simplest model of an exponential rate of conjecture
proof with a rate of 0.01/year for the dataset that we have studied,
translating into an average waiting time to proof of 100 years. We hope that
the presented methodology, combining the mathematics of recurrent processes,
linking proved and still open conjectures, with different empirical
constraints, will be useful for other similar investigations probing the
productivity associated with mankind growth and creativity.
1
vote
Anita Mehta
posted by Matúš Medo (14 February 2012)
We present a model of predatory traders interacting with each other in the
presence of a central reserve (which dissipates their wealth through say,
taxation), as well as inflation. This model is examined on a network for the
purposes of corre
6cd
lating complexity of interactions with systemic risk. We
suggest the use of selective networking to enhance the survival rates of
arbitrarily chosen traders. Our conclusions show that networking with 'doomed'
traders is the most risk-free scenario, and that if a trader is to network with
peers, it is far better to do so with those who have less intrinsic wealth than
himself to ensure individual, and perhaps systemic stability.
1
vote
Michael C. Münnix, Takashi Shimada, Rudi Schäfer, Francois Leyvraz Thomas H. Seligman, Thomas Guhr,
posted by Matúš Medo (14 February 2012)
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.
<br />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.
1
vote
Fulvio Baldovin, Francesco Camana, Massimiliano Caporin, Attilio L. Stella
posted by Matúš Medo (14 February 2012)
We demonstrate that a stochastic model consistent with the scaling properties
of financial assets is able to replicate the empirical statistical properties
of the S&P 500 high frequency data within a window of three hours in each
trading day. This result extends previous findings obtained for EUR/USD
exchange rates. We apply the forecast capabilities of the model to implement an
explicit trading strategy. Trading signals are model-based and not derived from
chartist criteria. In-sample and out-of-sample tests indicate that the model
performs better than a benchmark asymmetric GARCH process, and expose the
existence of small arbitrage opportunities. We discuss how to improve
performances and why the trading strategy is potentially interesting to hedge
volatility risk for S&P index-based products.
1
vote
Karissa McKelvey, Alex Rudnick, Michael D. Conover, Filippo Menczer
posted by Matúš Medo (14 February 2012)
The broad adoption of the web as a communication medium has made it possible
to study social behavior at a new scale. With social media networks such as
Twitter, we can collect large data sets of online discourse. Social science
researchers and journalists, however, may not have tools available to make
sense of large amounts of data or of the structure of large social networks. In
this paper, we describe our recent extensions to Truthy, a system for
collecting and analyzing political discourse on Twitter. We introduce several
new analytical perspectives on online discourse with the goal of facilitating
collaboration between individuals in the computational and social sciences. The
design decisions described in this article are motivated by real-world use
cases developed in collaboration with colleagues at the Indiana University
School of Journalism.
1
vote
Neil Johnson, Guannan Zhao, Eric Hunsader, Jing Meng, Amith Ravindar, Spencer Carran, Brian Tivnan
posted by Matúš Medo (14 February 2012)
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.
1
vote
Xin Shuai, Alberto Pepe, Johan Bollen
posted by Matúš Medo (14 February 2012)
We analyze the online response of the scientific community to the preprint
publication of scholarly articles. We employ a cohort of 4,606 scientific
articles submitted to the preprint database arXiv.org between October 2010 and
April 2011. We study three forms of reactions to these preprints: how they are
downloaded on the arXiv.org site, how they are mentioned on the social media
site Twitter, and how they are cited in the scholarly record. We perform two
analyses. First, we analyze the delay and time span of article downloads and
Twitter mentions following submission, to understand the temporal configuration
of these reactions and whether significant differences exist between them.
Second, we run correlation tests to investigate the relationship between
Twitter mentions and both article downloads and article citations. We find that
Twitter mentions follow rapidly after article submission and that they are
correlated with later article downloads and later article citations, indicating
that social media may be an important factor in determining the scientific
impact of an article.
1
vote
M. Puck Rombach, Mason A. Porter, James H. Fowler, Peter J. Mucha
posted by Matúš Medo (14 February 2012)
Intermediate-scale (or 'meso-scale') structures in networks have received
considerable attention, as the algorithmic detection of such structures makes
it possible to discover network features that are not apparent either at the
local scale of nodes and edges or at the global scale of summary statistics.
Numerous types of meso-scale structures can occur in networks, but
investigations of meso-scale network features have focused predominantly on the
identification and study of community structure. In this paper, we develop a
new method to investigate the meso-scale feature known as coreperiphery
structure, which consists of an identification of a network's nodes into a
densely connected core and a sparsely connected periphery. In contrast to
traditional network communities, the nodes in a core are also reasonably
well-connected to those in the periphery. Our new method of computing
core-periphery structure can identify multiple cores in a network and takes
different possible cores into account, thereby enabling a detailed description
of core-periphery structure. We illustrate the differences between our method
and existing methods for identifying which nodes belong to a core, and we use
it to classify the most important nodes using examples of friendship,
collaboration, transportation, and voting networks.
1
vote
G. Cadogan
posted by gocadog (14 February 2012)
This note is based on a recent confidence index introduced in the context of compensating probability factors for deviations of subjective probability measures from equivalent martingale measures. The index is adjusted for loss gain probability spreads, and it explains momentum in confidence. We introduce a confidence matrix operator which shows how a subject transforms gain domain into fear of loss. So she is loss averse or risk averse. By contrast, the adjoint confidence matrix operator is an Euclidean motion which rotates and reverses loss domain into hope of gain. Thus, signifying risk seeking over loss domains in hope of gain. Simulation of the model shows that the distribution of loss [gain] probabilities is a predictor of confidence momentum. It supports the trajectories of random fields of confidence which portend a term structure of confidence for hope and fear. Our theory explains why“irrational exuberance” and market confidence predict bubbles and crashes. It plainly shows that the growth rate of popular confidence indexes like UBS/Gallup Investor Optimism Index; Michigan Consumer Confidence Index; and Yale Investor Confidence Index predict bubbles and crashes.
1
vote
Dror Y. Kenett, Matthias Raddant, Thomas Lux, and Eshel Ben-Jacob
posted by Dror Kenett (9 February 2012)
Background: In the current era of strong worldwide market couplings the global financial village became highly prone to systemic collapses, events that can rapidly sweep throughout the entire village.
Methodology/Principal Findings: We present a new methodology to assess and quantify inter-market relations. The approach is based on the correlations between the market index, the index volatility, the market Index Cohesive Force and the meta-correlations (correlations between the intra-correlations.) We investigated the relations between six important world markets—U.S., U.K., Germany, Japan, China and India—from January 2000 until December 2010. We found that while the developed ‘‘western’’ markets (U.S., U.K., Germany) are highly correlated, the interdependencies between these markets and the developing ‘‘eastern’’ markets (India and China) are volatile and with noticeable maxima at times of global world events. The Japanese market switches ‘‘identity’’—it switches between periods of high meta-correlations with the ‘‘western’’ markets and periods when it behaves more similarly to the ‘‘eastern’’ markets.
Conclusions/Significance: The methodological framework presented here provides a way to quantify the evolvement of interdependencies in the global market, evaluate a world financial network and quantify changes in the world inter market relations. Such changes can be used as precursors to the agitation of the global financial village. Hence, the new approach can help to develop a sensitive ‘‘financial seismograph’’ to detect early signs of global financial crises so they can be treated before they develop into worldwide events.
1
vote
J. Shen, B. Zheng
posted by digudigu (4 February 2012)
With the daily and minutely data of the German DAX and Chinese indices, we
investigate how the return-volatility correlation originates in financial
dynamics. Based on a retarded volatility model, we may eliminate or generate
the return-volatility correlation of the time series, while other
characteri
83b
stics, such as the probability distribution of returns and long-range
time-correlation of volatilities etc., remain essentially unchanged. This
suggests that the leverage effect or anti-leverage effect in financial markets
arises from a kind of feedback return-volatility interactions, rather than the
long-range time-correlation of volatilities and asymmetric probability
distribution of returns. Further, we show that large volatilities dominate the
return-volatility correlation in financial dynamics.
1
vote
G. Cadogan
posted by gocadog (3 February 2012)
This paper contributes to the literature on decision making under risk and uncertainty by attaching a weighted probability space to outcome space. Thereby inducing a commutative map of behaviour on prospect theory's function space. We endow that space with a psychological metric space, and a time dependent probability density function with kurtosis controlled by a subject's strength of preference. Several new results are derived on that behavioural topological apparatus. First, we prove that gambles are random fields over outcome space. In which case, an uncertain prospect or act is akin to an unobserved configuration of a random field. Second, we introduce a priority heuristic result by proving that a subject's confidence evolves like a stopped behavioral stochastic process depicted by behavior mimicking $\epsilon$-homotopy of a fair gamble, i.e. a martingale. There, we use Dudley-Talagrand metric to characterize large deviation probabilities for the stopped process. Third, we introduce an impossibility theorem for equivalent martingale measures on psychological space--which explains why subjects gamble with over or under confidence almost surely. Fourth, we show that even when subjects have Von Neuman Morgenstern preferences, and know \emph{ex ante} that the gamble is fair, they still exhibit confident behavior due to the commmon consequence of probability leakage arising from measurement error--a \emph{de facto} priority heuristic. Fifth, our model mitigates critique of constructive choice models which allege that expected-utility models, and prospect theory, are unable to explain anomalous results that deviate from actuarially fair gambles.
1
vote
J. Shen, B. Zheng
posted by digudigu (3 February 2012)
To investigate the universal structure of interactions in financial dynamics,
we analyze the cross-correlation matrix C of price returns of the Chinese stock
market, in comparison with those of the American and Indian stock markets. As
an important emerging market, the Chinese market exhibits much stronger
correlations than the developed markets. In the Chinese market, the
interactions between the stocks in a same business sector are weak, while extra
interactions in unusu
6b9
al sectors are detected. Using a variation of the
two-factor model, we simulate the interactions in financial markets.
2
votes
Małgorzata Snarska
posted by Matúš Medo (1 February 2012)
74c
We show how random matrix theory can be applied to develop new algorithms to
extract dynamic factors from macroeconomic time series. In particular, we
consider a limit where the number of random variables N and the number of
consecutive time measurements T are large but the ratio N / T is fixed. In this
regime the underlying random matrices are asymptotically equivalent to Free
Random Variables (FRV).Application of these methods for macroeconomic
indicators for Poland economy is also presented.
2
votes
Alina Beygelzimer, John Langford, David Pennock
posted by Matúš Medo (1 February 2012)
In evaluating prediction markets (and other crowd-prediction mechanisms),
investigators have repeatedly observed a so-called "wisdom of crowds" effect,
which roughly says that the average of participants performs much better than
the average participant. The market price---an average or at least aggregate of
traders' beliefs---offers a better estimate than most any individual trader's
opinion. In this paper, we ask a stronger question: how does the market price
compare to the best trader's belief, not just the average trader. We measure
the market's worst-case log regret, a notion common in machine learning theory.
To arrive at a meaningful answer, we need to assume something about how traders
behave. We suppose that every trader optimizes according to the Kelly criteria,
a strategy that provably maximizes the compound growth of wealth over an
(infinite) sequence of market interactions. We show several consequences.
First, the market prediction is a wealth-weighted average of the individual
participants' beliefs. Second, the market learns at the optimal rate, the
market price reacts exactly as if updating according to Bayes' Law, and the
market prediction has low worst-case log regret to the best individual
participant. We simulate a sequence of markets where an underlying true
probability exists, showing that the market converges to the true objective
frequency as if updating a Beta distribution, as the theory predicts. If agents
adopt a fractional Kelly criteria, a common practical variant, we show that
agents behave like full-Kelly agents with beliefs weighted between their own
and the market's, and that the market price converges to a time-discounted
frequency. Our analysis provides a new justification for fractional Kelly
betting, a strategy widely used in practice for ad-hoc reasons. Finally, we
propose a method for an agent to learn her own optimal Kelly fraction.
3
votes
X.F. Jiang, B. Zheng
posted by Matúš Medo (1 February 2012)
With the random matrix theory, we study the spatial structure of the Chinese
stock market, American stock market and global market indices. After taking
into account the signs of the components in the eigenvectors of
7a7
the
cross-correlation matrix, we detect the subsector structure of the financial
systems. The positive and negative subsectors are anti-correlated each other in
the corresponding eigenmode. The subsector structure is strong in the Chinese
stock market, while somewhat weaker in the American stock market and global
market indices. Characteristics of the subsector structures in different
markets are revealed.
1
vote
Martin Gremm, Mark B. Wise
posted by Matúš Medo (1 February 2012)
Social Security and other public policies can be viewed as a series of cash
in and outflows that depend on parameters such as the age distribution of the
population and the retirement age. Given forecasts of these parameters,
policies can be designed to be financially stable, i.e., to terminate with a
zero balance. If reality deviates from the forecasts, policies normally
te
657
rminate with a surplus or a deficit. We derive constraints on the cash flows
of robust policies that terminate with zero balance even in the presence of
forecasting errors. Social Security and most similar policies are not robust.
We show that non-trivial robust policies exist and provide a recipe for
constructing robust extensions of non-robust policies. An example illustrates
our results.
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