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 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.

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 721 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.

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.

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.

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.

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.

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 7f8 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.