Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Netrin-1 Peptide Is a Chemorepellent in \u3cem\u3eTetrahymena thermophila\u3c/em\u3e

Netrin-1 is a highly conserved, pleiotropic signaling molecule that can serve as a neuronal chemorepellent during vertebrate development. In vertebrates, chemorepellent signaling is mediated through the tyrosine kinase, src-1, and the tyrosine phosphatase, shp-2. Tetrahymena thermophila has been used as a model system for chemorepellent signaling because its avoidance response is easily characterized under a light microscope. Our experiments showed that netrin-1 peptide is a chemorepellent in T. thermophila at micromolar concentrations. T. thermophila adapts to netrin-1 over a time course of about 10 minutes. Netrin-adapted cells still avoid GTP, PACAP-38, and nociceptin, suggesting that netrin does not use the same signaling machinery as any of these other repellents. Avoidance of netrin-1 peptide was effectively eliminated by the addition of the tyrosine kinase inhibitor, genistein, to the assay buffer; however, immunostaining using an anti-phosphotyrosine antibody showed similar fluorescence levels in control and netrin-1 exposed cells, suggesting that tyrosine phosphorylation i s not required for signaling to occur. In addition, ELISA indicates that a netrin-like peptide is present in both whole cell extract and secreted protein obtained from Tetrahymena thermophila. Further study will be required in order to fully elucidate the signaling mechanism of netrin-1 peptide in this organism

Discrete-time volatility forecasting with persistent leverage effect and the link with continuous-time volatility modeling

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models that are able to reproduce the statistical features captured by the discrete-time model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multifactor Markovian model fully replicates the persistence of both volatility and leverage effect. The impact of jumps can be associated with a common jump component in price and volatility

Agglomeration, Inequality and Economic Growth (WP)

The impact of income inequality on economic growth is dependent on several factors, including the time horizon considered, the initial level of income and its initial distribution. Yet, as growth and inequality are also uneven across space, it is also pertinent to consider the effects of the geographical agglomeration of economic activity. Moreover, it would also seem pertinent to consider not just the levels of inequality and agglomeration, but also the changes they undergo -i.e., their within-country evolution- and how these two processes interact with each other. By applying different econometric specifications and by introducing different measures of agglomeration at country level -specifically, urbanization and urban concentration rates-, this study analyzes how inequality and agglomeration -both their levels and their evolution- influence economic growth in function of the country’s level of development and its initial income distribution. Our results suggest, in line with previous studies, that while high inequality levels are a limiting factor for long-run growth, increasing inequality and increasing agglomeration have the potential to enhance growth in low-income countries where income distribution remains relatively equal, but can result in congestion diseconomies in high-income countries, especially if income distribution becomes particularly unequal

Analogy making and the structure of implied volatility skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew