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.
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
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al sectors are detected. Using a variation of the
two-factor model, we simulate the interactions in financial markets.
Małgorzata Snarska
posted by Matúš Medo
(1 February 2012)
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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.
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.
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
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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.
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.
Lukas Vacha, Jozef Barunik
posted by LKristoufek
(31 January 2012)
In this paper, we contribute to the literature on energy mar
967
ket co-movement
by studying its dynamics in the time-frequency domain. The novelty of our
approach lies in the application of wavelet tools to commodity market data. A
major part of economic time series analysis is done in the time or frequency
domain separately. Wavelet analysis combines these two fundamental approaches
allowing study of the time series in the time- frequency domain. Using this
framework, we propose a new, model-free way of estimating time-varying cor-
relations. In the empirical analysis, we connect our approach to the dynamic
conditional correlation approach of Engle (2002) on the main components of the
energy sector. Namely, we use crude oil, gasoline, heating oil, and natural gas
on a nearest-future basis over a period of approximately 16 and 1/2 years
beginning on November 1, 1993 and ending on July 21, 2010. Using wavelet
coherence, we uncover interesting dynamics of correlations between energy
commodities in the time-frequency space.
Jozef Barunik, Ladislav Kristoufek
posted by LKristoufek
(31 January 2012)
In this paper, we show how the sampling properties of the Hurst exponent
methods of estimation change with the presence of heavy tails. We run extensive
Monte Carlo simulations to find out how rescaled range analysis (R/S),
multifractal detrended fluctuation analysis (MF-DFA), detrending moving average
(DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on
independent series with different heavy tails. For this purpose, we generate
independent random series from stable distribution with stability exponent
{\alpha} changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution)
and we estimate the Hurst exponent using the different methods. R/S and GHE
prove to be robust to heavy tails in the underlying process. GHE provides the
lowest variance and bias in comparison to the other methods regardless the
presence of heavy tails in data and sample size. Utilizing this result, we
apply a novel approach of the intraday time-dependent Hurst exponent and we
estimate the Hurst exponent on high frequency data for each trading day
separately. We obtain Hurst exponents for S&P500 index for the period beginning
with year 1983 and ending by November 2009 and we discuss the surprising result
which uncovers how the market's behavior changed over this long period.
Jozef Barunik, Lukas Vacha
posted by LKristoufek
(31 January 2012)
In this paper we propose a new approach to estimation of the tail exponent in
financial stock markets. We begin the study with the finite sample behavior of
the Hill estimator under {\alpha}-stable distributions. Using large Monte Carlo
simulations, we show that the Hill estimator overestimates the true tail
exponent and can hardly be used on samples with small length. Utilizing our
results, we introduce a Monte Carlo-based method of estimation for the tail
exponent. Our proposed method is not sensitive to the choice of tail size an
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d
works well also on small data samples. The new estimator also gives unbiased
results with symmetrical confidence intervals. Finally, we demonstrate the
power of our estimator on the international world stock market indices. On the
two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent.
Jongwook Kim, Gabjin Oh
posted by Matúš Medo
(31 January 2012)
We propose a stochastic process driven by memory effect with novel
distributions including both exponential and leptokurtic heavy-tailed
distributions. A class of distribution is analytically derived from the
continuum limit of the discrete binary process with the renormalized
auto-correlation and the closed form moment generating function is obtained,
thus the cumulants are calculated and shown to be convergent. The other class
of distributions are numerically investigated. The concoction of the two
stochastic processes of the different s
527
igns of memory under regime switching
mechanism does incarnate power-law decay behavior, which strongly implies that
memory is the alternative origin of heavy-tail.
Peter Kratz, Torsten Schöneborn
posted by Matúš Medo
(31 January 2012)
We consider an illiquid financial market where a risk-averse investor has to
liquidate a large portfolio within a finite time horizon [0,T] and can trade
continuously at a traditional exchange (the "primary venue") and in a dark
pool. At the primary venue, trading yields a linea
956
r price impact. In the dark
pool, no price impact costs arise but order execution is uncertain, modeled by
a multi-dimensional Poisson process. We characterize the costs of trading by a
linear-quadratic functional which incorporates both the price impact costs of
trading at the primary exchange and the market risk of the position. The
liquidation constraint implies a singularity of the value function of the
resulting minimization problem at the terminal time T. Via the HJB equation and
a quadratic ansatz, we obtain a candidate for the value function which is the
limit of a sequence of solutions of initial value problems for a matrix
differential equation. Although the differential equation is not a Riccati
equation, we are able to show that this limit exists by using an appropriate
matrix inequality and a comparison result for Riccati equations. Additionally,
we obtain upper and lower bounds of the solutions of the initial value
problems, which allow us to prove a verification theorem. If a single asset
position is to be liquidated, the investor slowly trades out of her position at
the primary venue, with the remainder being placed in the dark pool at any
point in time. For multi-asset liquidations this is generally not optimal, and
the optimal strategy depends strongly on the correlation of the assets.
Anne-Ly Do, Lars Rudolf, Thilo Gross
posted by Matúš Medo
(31 January 2012)
In a recent paper, we analyzed the self-assembly of a complex cooperation
network. The network was shown to approach a state, where every agent invests
the same amount of resources. Nevertheless, highly-connected agents arise that
extract extra-ordinarily high payoffs while contributing comparably little to
any of their cooperations. Here, we investigate a variant of the model, in
which highly-connected agents have access to additional resources. We study
analytically and numerically whether these resources are invested in existing
collaborations, leading to a fairer load distribution, or in establishing new
collaborations, leading to an even less fair distribution of loads and payoffs.
B. Berche, C. von Fer
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ber, T. Holovatch, Yu. Holovatch
posted by Matúš Medo
(31 January 2012)
The goals of this paper are to present criteria, that allow to a priori
quantify the attack stability of real world correlated networks of finite size
and to check how these criteria correspond to analytic results available for
infinite uncorrelated networks. As a case study, we consider public
transportation networks (PTN) of several major cities of the world. To analyze
their resilience against attacks either the network nodes or edges are removed
in specific sequences (attack scenarios). During each scenario the size S(c) of
the largest remaining network component is observed as function of the removed
share c of nodes or edges. To quantify the PTN stability with respect to
different attack scenarios we use the area below the curve described by S(c)
for c \in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011)
3838) as a numerical measure of network robustness. This measure captures the
network reaction over the whole attack sequence. We present results of the
analysis of PTN stability against node and link-targeted attacks.
M. Dickison, S. Havlin, H. E. Stanley
posted by Matúš Medo
(31 January 2012)
Populations are seldom completely isolated from their environment.
Individuals in a particular geographic or social region may be considered a
distinct network due to strong
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local ties, but will also interact with
individuals in other networks. We study the susceptible-infected-recovered
(SIR) process on interconnected network systems, and find two distinct regimes.
In strongly-coupled network systems, epidemics occur simultaneously across the
entire system at a critical infection strength $\beta_c$, below which the
disease does not spread. In contrast, in weakly-coupled network systems, a
mixed phase exists below $\beta_c$ of the coupled network system, where an
epidemic occurs in one network but does not spread to the coupled network. We
derive an expression for the network and disease parameters that allow this
mixed phase and verify it numerically. Public health implications of
communities comprising these two classes of network systems are also mentioned.