A BLACK－SCHOLES FORMULA FOR OPTIONPRICINGWITHDIVIDENDS

We obtain a Black Scholes formula for the arbitrage free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow money form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. The corresponding Black Scholes formula is given. We notice that it is in fact the borrowing rate that plays the role in the pricing formula.

Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering

Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.

Vacuum Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.

The modulating of Qingguang’anⅡFormula on gut microbiota in mice with chronic high intraocular pressure by 16S rDNA sequencing

Objective To investigate the effects of Qingguang'anⅡFormula(QGAⅡ)on the gut micro-biota of mice with chronic high intraocular pressure(IOP)model,and explore its key micro-biota for protecting the optic nerve.Methods A total of 10 specific pathogen free(SPF)grade female DBA/2J mice were random-ly divided into model group and QGAⅡgroup(n=5 for each group),while additional 5 SPF-grade female C57BL/6J mice were assigned to control group.Mice presented spontaneous high IOP and showed elevated approximately at the age of seven months.The high IOP was maintained until week 38,when gavage was initiated.Mice in control group underwent the same intragastric treatment,while those in QGAⅡgroup were gavaged with QGAⅡ(9.67 g/kg),once a day for four weeks.Retinal morphology was examined using hematoxylin and eosin(HE)staining,with the number of retinal ganglion cells(RGCs)counted.The expression level of Brn3a protein,a specific marker for RGCs,was detected by immunofluorescence,with the mean optical density(OD)measured for quantitative analysis.In addition,16S rDNA se-quencing was leveraged to analyze changes in the diversity of gut microbiota,including theirα-diversity(Chao1,Shannon,Pielou’s evenness,and observed species index)andβ-diversity.Venn diagrams and linear discriminant analysis effect size(LEfSe)analysis was employed to investigate the number of amplicon sequence variants(ASVs),the abundance of differential gut microbiota species,and the classification of species at both the phylum and genus levels within the three groups of mice.Results HE staining revealed that compared with control group,model group showed signif-icant reduction in the number of RGCs(P<0.01),with intracellular vacuolar degeneration and nuclear pyknosis.After QGAⅡtreatment,the number of RGCs was significantly in-creased compared with model group(P<0.01),with notable improvements in intracellular vacuolar degeneration.Immunofluorescence analysis showed that the mean OD of Brn3a protein was significantly decreased in model group compared with control group(P<0.01),while QGAⅡtreatment significantly elevated its expression level(P<0.01).Analysis ofα-diversity showed that after QGAⅡintervention,the Chao1,Shannon,and Pielou’s evenness indices were significantly increased(P<0.01),and the observed species index was elevated(P<0.05).β-Diversity analysis demonstrated distinct clustering among the three groups,indicating relatively low similarity in bacterial community structures.ASV clustering identi-fied a total of 14061 ASVs across all groups,with 9514 ASVs shared between model and QGAⅡgroups.At the phylum level,the abundance of Bacteroidetes was significantly decreased in model group compared with control group(P<0.01),while Firmicutes and the Firmicutes/Bacteroidetes(F/B)ratio were significantly increased(P<0.01).QGAⅡtreatment significantly reduced both Firmicutes abundance and the F/B ratio(P<0.01).At the genus level,Lactobacillus was dominant across all groups,with its abundance significantly in-creased in model group(P<0.01)and subsequently decreased following QGAⅡintervention(P<0.05).Conclusion QGAⅡrestructured the gut microbiota of DBA/2J mice with chronic high IOP,bringing changes in their diversity and abundance of components.Firmicutes,Bacteroidetes,Lactobacillus,along with their associated microorganisms,are likely critical components of the gut microbiota that contribute to the optic neuroprotective effects of QGAⅡon chronic high IOP mice.

Digital Disparities:How Artificial Intelligence Can Facilitate Anti-Black Racism in the U.S.Healthcare Sector

This paper delves into the intricate interplay between artificial intelligence(AI)systems and the perpetuation of Anti-Black racism within the United States medical industry.Despite the promising potential of AI to enhance healthcare outcomes and reduce disparities,there is a growing concern that these technologies may inadvertently/advertently exacerbate existing racial inequalities.Focusing specifically on the experiences of Black patients,this research investigates how the following AI components:medical algorithms,machine learning,and natural learning processes are contributing to the unequal distribution of medical resources,diagnosis,and health care treatment of those classified as Black.Furthermore,this review employs a multidisciplinary approach,combining insights from computer science,medical ethics,and social justice theory to analyze the mechanisms through which AI systems may encode and reinforce racial biases.By dissecting the three primary components of AI,this paper aims to present a clear understanding of how these technologies work,how they intersect,and how they may inherently perpetuate harmful stereotypes resulting in negligent outcomes for Black patients.Furthermore,this paper explores the ethical implications of deploying AI in healthcare settings and calls for increased transparency,accountability,and diversity in the development and implementation of these technologies.Finally,it is important that I prefer the following paper with a clear and concise definition of what I refer to as Anti-Black racism throughout the text.Therefore,I assert the following:Anti-Black racism refers to prejudice,discrimination,or antagonism directed against individuals or communities of African descent based on their race.It involves the belief in the inherent superiority of one race over another and the systemic and institutional practices that perpetuate inequality and disadvantage for Black people.Furthermore,I proclaim that this form of racism can be manifested in various ways,such as unequal access to opportunities,resources,education,employment,and fair treatment within social,economic,and political systems.It is also pertinent to acknowledge that Anti-Black racism is deeply rooted in historical and societal structures throughout the U.S.borders and beyond,leading to systemic disadvantages and disparities that impact the well-being and life chances of Black individuals and communities.Addressing Anti-Black racism involves recognizing and challenging both individual attitudes and systemic structures that contribute to discrimination and inequality.Efforts to combat Anti-Black racism include promoting awareness,education,advocacy for policy changes,and fostering a culture of inclusivity and equality.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

The Black Protests in Poland: An Example of an Anti-pastoral Revolution

Michel Foucault in Security, Territory, Population: Lectures at the Collège de France, 1977-1978 argues, that there has never been such a thing as an anti-pastoral revolution in Western societies. Yes, we have had revolutions against the disciplinary apparatus and legal devices of power (schools, hospitals, prisons) and we have had examples of revolutions against the economic foundations of social inequality, but there has never been a genuine revolution against pastoral power as a power relating to the conduct of individuals (but also entire social groups) and their disposition to “voluntary submission” to the will of external authorities. In my paper, I would like to reflect on this thesis, and taking it quite seriously, to look for examples of such revolutions. One of them is a women’s strike in Poland during the power of the conservative government of “Law and Justice”. Mainly referring to the texts of Silvia Federici and Paul Preciado, I will want to reflect on contemporary practices of reclaiming the body in contemporary capitalism. I will defend the thesis that regaining control over sexuality and reproduction means changing the material conditions of life and modern reproductive technologies.

Vacum Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein's GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.

An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy

We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.

New Color-Difference Formula Based on CIECAM97s

To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new formula is then deduced in the space and named CDF CIECAM97s. The factors for lightness, chroma and hue correction in the formula are derived by linear regression according to BFD? CP data sets. It is found by statistical analysis that CDF CIECAM97s is in closer accordance with the visual assessments when compared with CMC(1∶1), CIE94 and CIE L *a *b * color difference formulae. Based on color appearance model, the new color difference formula can be used to predict color difference perception in a varity of different viewing conditions.

基于Ackermann's formula的类反斜线回滞系统滑模控制

回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然是个研究的领域,针对类反斜线回滞系统进行研究。把类反斜线回滞模型分解为确定的线性部分和已知上界的不确定非线性部分,利用Ackermann's formula给出了类反斜线回滞系统的滑模控制律。仿真表明此滑模控制律是有效的,同时此滑模控制保证了整个系统的稳定性。

基于Black-Scholes模型的期权定价新方法

考虑到实际金融市场的不完备性以及收益率分布的厚尾性,基于经典Black-Scholes模型并运用函数的下凸性,期权定价公式H(a)=E[(X-a)2]被推广为Hk(a)=E[(X-a)2k].通过DJSH(道琼斯上海)指数收益率的GARCH模型,并使用随机模拟的方法对这两个公式进行定价比较.结果表明这种方法有效提高了定价,从而降低了风险.

非线性Black-Scholes模型下利差期权定价

研究了原生资产价格遵循非线性Black-Scholes模型时的利差期权定价问题.利用扰动理论中单参数摄动展开方法,给出了利差期权的近似定价公式.最后,结合Feyman-Kac公式分析了近似定价公式的误差估计问题,结果表明近似解一致收敛于相应期权价格的精确解.

证券估值Black-Scholes模型的一般化(英文)

本文研究证券估值Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ 模型的一般化．一般化模型推导偏微分方程，然后用分离变量法考虑抛物型方程的Ｃａｕｃｈｙ

期权定价Black-scholes公式的一个新推导

文章提出Black-scholes公式的一个新推导.在风险中性定价的框架下,通过对正态分布的性质及其矩母函数的熟练运用,可以快速容易地导出Black-scholes公式.并且在此推导过程中,公式中的概率值Φ(d1),Φ(d2)的含义得以明确体现.

S4B-2 Bushen-Yizhi Formula Inhibits the NLRP3/NFκB Mediated Neuroinflammation and Improves the Motor Dysfunction in a Mouse Model of Parkinson’s Disease

Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TCM theory understanding,so we can learn from each other in the process of drug discovery.The clinical results showed that Bushen-Yizhi formula(BSYZ)could effectively improve the neurological function score of senile dementia patients and had a better anti-dementia effect.Further pharmacological studies showed that BSYZ had neuroprotective effects,such as anti-inflammatory,anti-oxidation,anti-apoptosis and neurotrophic effects.In this study,the therapeutic effect of BSYZ on PD was evaluated in vivo and in vivo,and its molecular mechanism was discussed in order to expand the scope of application of BSYZ and to provide strategies for drug discovery of related neurodegenerative diseases.Methods:C57 BL/6 mice were injected intraperitoneally with MPTP to construct a PD mouse model.BSYZ(1.46,2.92,5.84 mg·kg-1)was administered for two weeks,and the positive control group was given a NSAID,piroxicam(12.5 mg·kg-1).After 1 week of pretreatment,MPTP was used to construct a PD mouse model.The mice were subjected to Rotation test on days 1,3 and 5,6th day.and the movement coordination and exercise ability of the drug on PD mice were observed on theThe number of TH-positive cells,Iba1 and CD68-labeled microglial cells in SNpc region were observed by immunofluorescence to observe the proliferation and activation of microglial cells and GFAP-labeled astrocytes.Western blotting was used to detect the nuclear transfer of NLRP3,Caspase-1,ASC,pro-IL-1β,IL-1βand NF-κB in the midbrain.Results:1.BSYZ could significantly improve the expression of MPTP model mice in the experiment of fatigue and Y-maze,increase the number of neurons in SNpc region and the positive expression of TH protein.2.BSYZ significantly inhibited the number of Iba1/CD68-positive microglial cells in MPTP-model mice and decreased the number of GFAP-positive astrocytes.3.BSYZ significantly inhibited the expression of NLRP3-associated protein in BV2 microglial cells induced by LPS+ATP and inhibited the nuclear transfer of NF-κB.Conclusion:BSYZ can effectively relieve the motor dysfunction of PD model mice,improve the damage of dopaminergic neurons,inhibit the proliferation and activation of microglial cells and astrocytes,and have good anti-MPTPinduced neuroinflammation and neuroinflammation mediated by nuclear transfer of NF-κB.The results show that BSYZ has a good prospect of anti-Parkinson’s disease and provides valuable drug discovery strategies for the related neurodegenerative diseases.

开关式Hurst指数分形Black-Scholes市场中的欧式期权定价

考虑标的资产价值服从几何分形布朗运动,但其Hurst指数以Poisson过程的方式在状态(H1<a)和状态(H2>a)之间随机的转换的开关式Hurst指数分形Black-scholes市场模型中的欧式期权定价问题.得到在此模型下欧式看涨期权定价公式;并对定价公式进行简单地定性分析.

基于欧式期权的Black-Scholes定价公式研究

波动率是期权定价中的一个重要参数,但Black-Schooles公式在σ=0时无意义。解释了当σ=0时的金融意义;利用无套利原理得到了当σ=0时欧式期权的定价公式,结合对冲方法和Ito公式推导了期权价格所满足的偏微分方程,并在极限意义下,证明了Black-Scholes公式对于σ=0时也成立,给出了波动率很小时期权价格的近似估计。

从Black—Scholes公式看宝钢期权的理论价格

本文首先给出了Black—Scholes公式的一个简单的证明;其次,利用Black—Scholes公式计算出宝钢期权的理论价格,分析了理论价格实际市场的价格差异及原因。

在风险中性的假设下求证Black-scholes公式

Black-scholes期权定价公式的推导过程相当复杂,需要用到随机过程和求解随机微分方程等较高深的数学工具,本文将在风险中性的假设下给出两种Black-scholes期权定价公式的简洁推导方法,使得具有概率统计和微积分基本知识的读者也能理解并欣赏这一公式的导出过程。