分类： 数学 >> 统计和概率 分类： 数学 >> 应用数学 提交时间： 2022-03-30
摘要： In this paper, we propose and study a novel continuous-time model,based on the well-known constant elasticity of variance (CEV) model,to describe the asset price process.The basic idea is that the volatility elasticity of the CEV model can not be treated as a constantfrom the perspective of stochastic analysis.To address this issue, we deduce the price process of assetsfrom the perspective of volatility elasticity,propose the constant volatility elasticity (CVE) model,and further derive a more general variable volatility elasticity (VVE) model.Moreover, our model can describe the positive correlation between volatility and asset pricesexisting in the commodity markets,while CEV model can only describe the negative correlation.Through the empirical research on the financial market,many assets, especially commodities,often show this positive correlation phenomenon in some time periods,which shows that our model has strong practical application value.Finally, we provide the explicit pricing formula of European optionsbased on our model.This formula has an elegant form convenient to calculate,which is similarly to the renowned Black-Scholes formulaand of great significance to the research of derivatives market.
分类： 核科学技术 >> 粒子加速器 提交时间： 2023-06-18 合作期刊: 《Nuclear Science and Techniques》
摘要： In this paper, we present a theoretical study on excitonic absorption spectra of one-dimensional semiconductor quantum wires. The carrier-carrier scattering is treated by the second Born approximation in the Markovian limit. The absorption spectra of different carrier densities and temperatures are discussed. The excitonic absorption peak position and width show complicated dependence on carrier density and temperature, indicating the importance of carrier-carrier scattering. The behavior can be understood by the cooperative effects of exchange self-energy and Coulomb correlation due to carrier-carrier scattering.
分类： 物理学 >> 地球物理学、天文学和天体物理学 提交时间： 2023-12-15 合作期刊: 《Research in Astronomy and Astrophysics》
摘要： Fermi-LAT LCR provides continuous and regularly sampled gamma-ray light curves, spanning about 14 yr, for a large sample of blazars. The log-normal flux distribution and linear rms–flux relation of the light curves for a few Fermi blazars have been examined in previous studies. However, the probability that blazars exhibit the log-normal flux distribution and linear rms–flux relation in their gamma-ray light curves has not been systematically explored. In this study, we comprehensively research the distribution of γ-ray flux and the statistical characteristics on a large sample of 1414 variable blazars from the Fermi-LAT LCR catalog, including 572 FSRQs, 477 BL Lacs, and 365 BCUs, and statistically compare their flux distributions with normal and log-normal distributions. The results indicate that the probability of not rejecting log-normal is 42.05% for the large sample, and there is still a 2.05% probability of not rejecting normality, based on the joint of Kolmogorov–Smirnov, Shapiro–Wilk, and Normality tests. We further find that the probability that BL Lacs conform to the log-normal distribution is higher than that of FSRQs. Besides, after removing sources with less than 200 data points from this large sample, a sample of 549 blazars, which is still a large sample compared to the previous studies, was obtained. Based on dividing the light curves into segments every 20 points (or 40 points, or one year), we fitted the linear rms–flux relation of these three different sets and found that the Pearson correlation coefficients are all close to 1 for most blazars. This result indicates a strong linear correlation between the rms and the flux of these 549 blazars. The log-normal distribution and linear rms–flux relation indicate that the variability of the γ-ray flux for most blazars is a non-linear and multiplicative process.
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