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.

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.

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.

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.

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.

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.

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 62c 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.

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.

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.

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 indepen 956 dent 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.