Iterated function systems with a given continuous stationary distribution

For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.Comment: 7 pages, 3 figure

Multiscaled Cross-Correlation Dynamics in Financial Time-Series

The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices over different timescales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different times and scales provides insight into the interactions between the numerous constituents involved. Eigenvalue dynamics are examined for both medium and high-frequency equity returns, with the associated correlation structure shown to be dependent on both time and scale. Additionally, the Epps effect is established using this multivariate method and analyzed at longer scales than previously studied. A partition of the eigenvalue time-series demonstrates, at very short scales, the emergence of negative returns when the largest eigenvalue is greatest. Finally, a portfolio optimization shows the importance of timescale information in the context of risk management

Managing Risk of Bidding in Display Advertising

In this paper, we deal with the uncertainty of bidding for display advertising. Similar to the financial market trading, real-time bidding (RTB) based display advertising employs an auction mechanism to automate the impression level media buying; and running a campaign is no different than an investment of acquiring new customers in return for obtaining additional converted sales. Thus, how to optimally bid on an ad impression to drive the profit and return-on-investment becomes essential. However, the large randomness of the user behaviors and the cost uncertainty caused by the auction competition may result in a significant risk from the campaign performance estimation. In this paper, we explicitly model the uncertainty of user click-through rate estimation and auction competition to capture the risk. We borrow an idea from finance and derive the value at risk for each ad display opportunity. Our formulation results in two risk-aware bidding strategies that penalize risky ad impressions and focus more on the ones with higher expected return and lower risk. The empirical study on real-world data demonstrates the effectiveness of our proposed risk-aware bidding strategies: yielding profit gains of 15.4% in offline experiments and up to 17.5% in an online A/B test on a commercial RTB platform over the widely applied bidding strategies

Portfolio Optimization and the Random Magnet Problem

Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movement of assets are are mutually correlated and therefore knowledge of cross--correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this ``random magnet problem'' are given by the cross-correlation matrix {\bf \sf C} of stock returns. We find that random matrix theory allows us to make an estimate for {\bf \sf C} which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.Comment: 12 pages, 4 figures, revte

Mortality risk and mental disorders: longitudinal results from the Upper Bavarian Study

The object of the study was the assessment of the mortality risk for persons with a mental disorder in an unselected representative community sample assessed longitudinally. Subjects from a rural area in Upper Bavaria (Germany) participated in semi-structured interviews conducted by research physicians in the 1970s (first assessment) and death-certificate diagnoses were obtained after an interval up to 13 years later. The sample consisted of 1668 community residents aged 15 years and over. Cox regression estimates resulted in an odds ratio of 1·35 (confidence interval 1·01 to 1·81) for persons with a mental disorder classified as marked to very severe. The odds ratio increased with increasing severity of mental illness from 1·04 for mild disorders, 1·30 for marked disorders, to 1·64 for severe or very severe disorders. The relative risk (odds ratio) for persons with a mental disorder only and no somatic disorder was 1·22, for persons with only a somatic disorder 2·00, and for those with both a mental and a somatic disorder 2·13. The presence of somatic illness was responsible for most of the excess mortality. Somatic disorders associated with excess mortality in mental disorders were diseases of the nervous system or sensory organs, diseases of the circulatory system, diseases of the gastrointestinal tract, and diseases of the skeleton, muscles and connective tissue (ICD-8). Thus, while mental illness alone had a limited effect on excess mortality, comorbidity with certain somatic disorders had a significant effec

Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text

Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Ground-state energies, densities and momentum distributions in closed-shell nuclei calculated within a cluster expansion approach and realistic interactions

A linked cluster expansion suitable for the treatment of ground-state properties of complex nuclei, as well as of various particle-nucleus scattering processes, has been used to calculate the ground-state energy, density and momentum distribution of 16-O and 40-Ca using realistic interactions. First of all, a benchmark calculation for the ground-state energy has been performed using the truncated V8' potential, and consisting in the comparison of our results with the ones obtained by the Fermi Hypernetted Chain approach, adopting in both cases the same mean field wave functions and the same correlation functions. The results exhibited a nice agreement between the two methods. Therefore, the approach has been applied to the calculation of the ground-state energy, density and momentum distributions of 16-O and 40-Ca using the full V8' potential, finding again a satisfactory agreement with the results based on more advanced approaches where higher order cluster contributions are taken into account. It appears therefore that the cluster expansion approach can provide accurate approximations for various diagonal and non diagonal density matrices, so that it could be used for a reliable evaluation of nuclear effects in various medium and high energy scattering processes off nuclear targets. The developed approach can be readily generalized to the treatment of Glauber type final state interaction effects in inclusive, semi-inclusive and exclusive processes off nuclei at medium and high energies.Comment: 42 pages, 18 figure

Distance perception in a natural outdoor setting: is there a developmental trend to overconstancy?

The main purpose of the present study was to investigate whether in natural environment, using very large physical distances, there is a trend to overconstancy for distance estimates during development. One hundred and twenty-nine children aged 5 to 13 years old and twenty-one adults (in a control group), participated as observers. The observer’s task was to bisect egocentric distances, ranging from 1.0 to 296.0 m, presented in a large open field. The analyses focused on two parameters, constant errors and variable errors, such as measuring accuracy and precision, respectively. A third analysis focused on the developmental pattern of shifts in constancy as a function of age and range of distances. Constant error analysis showed that there are two relevant parameters for accuracy, age, and range of distances. For short distances, there are three developmental stages: 5-7 years, when children have unstable responses, 7-11, underconstancy, and 13 to adulthood, when accuracy is reached. For large distances, there is a two-stage development: 5-11 years, with severe underconstancy, and beyond this age, with mild underconstancy. Variable errors analyses indicate that precision is noted for 7 year-old children, independently of the range of distances. The constancy analyses indicated that there is a shift from constancy (or slightly overconstancy) to underconstancy as a function of physical distance for all age groups. The age difference is noted in the magnitude of underconstancy that occurs in larger distances, where adults presented lower levels of underconstancy than children. The present data were interpreted as due to a developmental change in cognitive processing rather than to changes in visual space perception.El principal objetivo de este estudio fue investigar si en un medio natural, empleando distancias físicas muy grandes, hay una tendencia a sobre-constancia para las estimaciones de distancias durante el desarrollo evolutivo. Participaron como observadores 129 niños de edades entre 5 y 13 años y 21 adultos (en un grupo control). La tarea de los observadores consistió en biseccionar unas distancias egocéntricas, que variaban entre 1,0 y 296,0 m, presentadas en un gran campo abierto. El análisis se centró en dos parámetros, error constante y error variable, de la exactitud y precisión de medida, respectivamente. Un tercer análisis se centró en el patrón evolutivo de cambios en la constancia en función de la edad y el rango de distancias. El análisis de los errores constantes mostró que hay dos parámetros relevantes para la precisión, edad y rango de distancias. Para distancias cortas, hay tres fases evolutivas: 5-7 años, cuando los niños dan respuestas inestables, 7-11, infra-constancia, y 13 años hasta la adultez, cuando alcanzan la exactitud (constancia). Para las distancias largas, hay un desarrollo de dos fases: 5-11 años, con infra-constancia severa, y más allá de esta edad, con ligera infraconstancia. El análisis del error variable indica que se alcanza precisión a partir de 7 años, con independencia del rango de distancias. En análisis de la constancia indica que existe un cambio desde la constancia (o una ligera sobre-constancia) a infra-constancia en función de la distancia física para todos los grupos de edad. La diferencia de edad se nota en la magnitud de la infra-constancia que ocurre en las distancias más largas, donde los adultos presentaban niveles menores de infra-constancia que los niños. Estos datos se interpretan como debidos a un cambio evolutivo en el procesamiento cognitivo más que a cambios en la percepción visual del espacio

One-Dimensional and Multi-Dimensional Studies of the Exocentric Distance Estimates in Frontoparallel Plane, Virtual Space, and Outdoor Open Field

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