782 research outputs found
Leverage Causes Fat Tails and Clustered Volatility
We build a simple model of leveraged asset purchases with margin calls.
Investment funds use what is perhaps the most basic financial strategy, called
"value investing", i.e. systematically attempting to buy underpriced assets.
When funds do not borrow, the price fluctuations of the asset are normally
distributed and uncorrelated across time. All this changes when the funds are
allowed to leverage, i.e. borrow from a bank, to purchase more assets than
their wealth would otherwise permit. During good times competition drives
investors to funds that use more leverage, because they have higher profits. As
leverage increases price fluctuations become heavy tailed and display clustered
volatility, similar to what is observed in real markets. Previous explanations
of fat tails and clustered volatility depended on "irrational behavior", such
as trend following. Here instead this comes from the fact that leverage limits
cause funds to sell into a falling market: A prudent bank makes itself locally
safer by putting a limit to leverage, so when a fund exceeds its leverage
limit, it must partially repay its loan by selling the asset. Unfortunately
this sometimes happens to all the funds simultaneously when the price is
already falling. The resulting nonlinear feedback amplifies large downward
price movements. At the extreme this causes crashes, but the effect is seen at
every time scale, producing a power law of price disturbances. A standard
(supposedly more sophisticated) risk control policy in which individual banks
base leverage limits on volatility causes leverage to rise during periods of
low volatility, and to contract more quickly when volatility gets high, making
these extreme fluctuations even worse.Comment: 19 pages, 8 figure
Leverage Causes Fat Tails and Clustered Volatility
We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior," such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.Systemic risk, Clustered volatility, Fat tails, Crash, Margin calls, Leverage
Scaling-violation phenomena and fractality in the human posture control systems
By analyzing the movements of quiet standing persons by means of wavelet
statistics, we observe multiple scaling regions in the underlying body
dynamics. The use of the wavelet-variance function opens the possibility to
relate scaling violations to different modes of posture control. We show that
scaling behavior becomes close to perfect, when correctional movements are
dominated by the vestibular system.Comment: 12 pages, 4 figures, to appear in Phys. Rev.
Micromechanical model of bovine Haversian bone predicts strain amplification through soft interfaces
Context. Recent observations of brown dwarf spectroscopic variability in the infrared infer the presence of patchy cloud cover. Aims. This paper proposes a mechanism for producing inhomogeneous cloud coverage due to the depletion of cloud particles through the Coulomb explosion of dust in atmospheric plasma regions. Charged dust grains Coulomb-explode when the electrostatic stress of the grain exceeds its mechanical tensile stress, which results in grains below a critical radius a < aCoulcrit being broken up. Methods. This work outlines the criteria required for the Coulomb explosion of dust clouds in substellar atmospheres, the effect on the dust particle size distribution function, and the resulting radiative properties of the atmospheric regions. Results. Our results show that for an atmospheric plasma region with an electron temperature of Te = 10 eV (≈ 105 K), the critical grain radius varies from 10-7 to 10-4 cm, depending on the grains’ tensile strength. Higher critical radii up to 10-3 cm are attainable for higher electron temperatures. We find that the process produces a bimodal particle size distribution composed of stable nanoscale seed particles and dust particles with a ≥ aCoulcrit , with the intervening particle sizes defining a region devoid of dust. As a result, the dust population is depleted, and the clouds become optically thin in the wavelength range 0:1 - 10 μm, with a characteristic peak that shifts to higher wavelengths as more sub-micrometer particles are destroyed. Conclusions. In an atmosphere populated with a distribution of plasma volumes, this will yield regions of contrasting radiative properties, thereby giving a source of inhomogeneous cloud coverage. The results presented here may also be relevant for dust in supernova remnants and protoplanetary disks.PostprintPeer reviewe
On the robustness of q-expectation values and Renyi entropy
We study the robustness of functionals of probability distributions such as
the R\'enyi and nonadditive S_q entropies, as well as the q-expectation values
under small variations of the distributions. We focus on three important types
of distribution functions, namely (i) continuous bounded (ii) discrete with
finite number of states, and (iii) discrete with infinite number of states. The
physical concept of robustness is contrasted with the mathematically stronger
condition of stability and Lesche-stability for functionals. We explicitly
demonstrate that, in the case of continuous distributions, once unbounded
distributions and those leading to negative entropy are excluded, both Renyi
and nonadditive S_q entropies as well as the q-expectation values are robust.
For the discrete finite case, the Renyi and nonadditive S_q entropies and the
q-expectation values are robust. For the infinite discrete case, where both
Renyi entropy and q-expectations are known to violate Lesche-stability and
stability respectively, we show that one can nevertheless state conditions
which guarantee physical robustness.Comment: 6 pages, to appear in Euro Phys Let
Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency
We formulate three famous, descriptive essays of C.N. Parkinson on
bureaucratic inefficiency in a quantifiable and dynamical socio-physical
framework. In the first model we show how the use of recent opinion formation
models for small groups can be used to understand Parkinson's observation that
decision making bodies such as cabinets or boards become highly inefficient
once their size exceeds a critical 'Coefficient of Inefficiency', typically
around 20. A second observation of Parkinson - which is sometimes referred to
as Parkinson's Law - is that the growth of bureaucratic or administrative
bodies usually goes hand in hand with a drastic decrease of its overall
efficiency. In our second model we view a bureaucratic body as a system of a
flow of workers, which enter, become promoted to various internal levels within
the system over time, and leave the system after having served for a certain
time. Promotion usually is associated with an increase of subordinates. Within
the proposed model it becomes possible to work out the phase diagram under
which conditions bureaucratic growth can be confined. In our last model we
assign individual efficiency curves to workers throughout their life in
administration, and compute the optimum time to send them to old age pension,
in order to ensure a maximum of efficiency within the body - in Parkinson's
words we compute the 'Pension Point'.Comment: 15 pages, 5 figure
An extended formalism for preferential attachment in heterogeneous complex networks
In this paper we present a framework for the extension of the preferential
attachment (PA) model to heterogeneous complex networks. We define a class of
heterogeneous PA models, where node properties are described by fixed states in
an arbitrary metric space, and introduce an affinity function that biases the
attachment probabilities of links. We perform an analytical study of the
stationary degree distributions in heterogeneous PA networks. We show that
their degree densities exhibit a richer scaling behavior than their homogeneous
counterparts, and that the power law scaling in the degree distribution is
robust in presence of heterogeneity
Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?
Based on a rigorous extension of classical statistical mechanics to networks,
we study a specific microscopic network Hamiltonian. The form of this
Hamiltonian is derived from the assumption that individual nodes
increase/decrease their utility by linking to nodes with a higher/lower degree
than their own. We interpret utility as an equivalent to energy in physical
systems and discuss the temperature dependence of the emerging networks. We
observe the existence of a critical temperature where total energy
(utility) and network-architecture undergo radical changes. Along this
topological transition we obtain scale-free networks with complex hierarchical
topology. In contrast to models for scale-free networks introduced so far, the
scale-free nature emerges within equilibrium, with a clearly defined
microcanonical ensemble and the principle of detailed balance strictly
fulfilled. This provides clear evidence that 'complex' networks may arise
without irreversibility. The results presented here should find a wide variety
of applications in socio-economic statistical systems.Comment: 4 pages, 5 figure
Transport on complex networks: Flow, jamming and optimization
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics
Schumpeterian economic dynamics as a quantifiable minimum model of evolution
We propose a simple quantitative model of Schumpeterian economic dynamics.
New goods and services are endogenously produced through combinations of
existing goods. As soon as new goods enter the market they may compete against
already existing goods, in other words new products can have destructive
effects on existing goods. As a result of this competition mechanism existing
goods may be driven out from the market - often causing cascades of secondary
defects (Schumpeterian gales of destruction). The model leads to a generic
dynamics characterized by phases of relative economic stability followed by
phases of massive restructuring of markets - which could be interpreted as
Schumpeterian business `cycles'. Model timeseries of product diversity and
productivity reproduce several stylized facts of economics timeseries on long
timescales such as GDP or business failures, including non-Gaussian fat tailed
distributions, volatility clustering etc. The model is phrased in an open,
non-equilibrium setup which can be understood as a self organized critical
system. Its diversity dynamics can be understood by the time-varying topology
of the active production networks.Comment: 21 pages, 11 figure
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