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Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function 具有非线性波动函数的二维全非线性Black-Scholes方程的多重网格方法
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n3.20.02
Aicha Driouch Hassan Al Moatassime
{"title":"Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function","authors":"Aicha Driouch Hassan Al Moatassime","doi":"10.4208/jms.v53n3.20.02","DOIUrl":"https://doi.org/10.4208/jms.v53n3.20.02","url":null,"abstract":"This paper deals with the task of pricing European basket options in the presence of transaction costs. We develop a model that incorporates the illiquidity of the market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigrid method in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles’ and Soner’s model and to demonstrate the effectiveness of multigrid approach to solving a fully nonlinear two dimensional Black-Scholes problem. AMS subject classifications: 65N55, 65N06, 35K55, 65BXX","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46964284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations 非线性Dirac方程的（半）非相对极限
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n2.20.01
Yongyong Cai Yan Wang sci
{"title":"(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations","authors":"Yongyong Cai Yan Wang sci","doi":"10.4208/jms.v53n2.20.01","DOIUrl":"https://doi.org/10.4208/jms.v53n2.20.01","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43753957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting Dunkl环境下Orlicz空间上极大交换子的有界性
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n1.20.03
Vagif S. Guliyev sci
{"title":"Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting","authors":"Vagif S. Guliyev sci","doi":"10.4208/jms.v53n1.20.03","DOIUrl":"https://doi.org/10.4208/jms.v53n1.20.03","url":null,"abstract":"On the real line, the Dunkl operators Dν( f )(x) := d f (x) dx +(2ν+1) f (x)− f (−x) 2x , ∀x∈R, ∀ν≥− 1 2 are differential-difference operators associated with the reflection group Z2 on R, and on the Rd the Dunkl operators { Dk,j }d j=1 are the differential-difference operators associated with the reflection group Zd 2 on R d. In this paper, in the setting R we show that b ∈ BMO(R,dmν) if and only if the maximal commutator Mb,ν is bounded on Orlicz spaces LΦ(R,dmν). Also in the setting Rd we show that b∈ BMO(R,hk(x)dx) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ(R,hk(x)dx). AMS subject classifications: 42B20, 42B25, 42B35","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44376542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Regularity and Rigidity for Nonlocal Curvatures in Conformal Geometry 保形几何中非局部曲率的正则性和刚度
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n4.20.03
Wenxiong Zhang
{"title":"Regularity and Rigidity for Nonlocal Curvatures in Conformal Geometry","authors":"Wenxiong Zhang","doi":"10.4208/jms.v53n4.20.03","DOIUrl":"https://doi.org/10.4208/jms.v53n4.20.03","url":null,"abstract":"In this paper, we will explore the geometric effects of conformally covariant operators and the induced nonlinear curvature equations in certain nonlocal nature. Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42324423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and some Applications Gegenbauer微分算子卷积的O’Neil不等式及其应用
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n1.20.05
Vagif S. Guliyev sci
{"title":"O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and some Applications","authors":"Vagif S. Guliyev sci","doi":"10.4208/jms.v53n1.20.05","DOIUrl":"https://doi.org/10.4208/jms.v53n1.20.05","url":null,"abstract":"In this paper we prove an O’Neil inequality for the convolution operator (G-convolution) associated with the Gegenbauer differential operator Gλ. By using an O’Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the G-convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the G-fractional maximal and G-fractional integral operators from the spaces Lp,λ to Lq,λ and from the spaces L1,λ to the weak spaces WLp,λ. AMS subject classifications: 42B20, 42B25, 42B35, 47G10, 47B37","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46907558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods 用富集谱Galerkin方法对几个奇摄动问题和奇异积分方程的高精度数值逼近
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-06-01 DOI: 10.4208/jms.v53n2.20.02
Sheng Chen sci
{"title":"High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods","authors":"Sheng Chen sci","doi":"10.4208/jms.v53n2.20.02","DOIUrl":"https://doi.org/10.4208/jms.v53n2.20.02","url":null,"abstract":"Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods. AMS subject classifications: 65N35, 65R20, 41A30","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47831306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Solutions to the σk-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable 环uli上σk-Loewner-Nirenberg问题的解是局部Lipschitz且不可微的
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2020-01-13 DOI: 10.4208/JMS.V54N2.21.01
Yanyan Li, Luc Nguyen
{"title":"Solutions to the σk-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable","authors":"Yanyan Li, Luc Nguyen","doi":"10.4208/JMS.V54N2.21.01","DOIUrl":"https://doi.org/10.4208/JMS.V54N2.21.01","url":null,"abstract":"We show for $k geq 2$ that the locally Lipschitz viscosity solution to the $sigma_k$-Loewner-Nirenberg problem on a given annulus ${a frac{1}{k}$. Optimal regularity for solutions to the $sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48144176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
ODE Methods in Non-Local Equations 非局部方程中的ODE方法
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2019-10-31 DOI: 10.4208/jms.v53n4.20.01
Weiwei Ao, Hardy Chan, A. DelaTorre, M. Fontelos, Mar'ia de Mar Gonz'alez, Juncheng Wei
{"title":"ODE Methods in Non-Local Equations","authors":"Weiwei Ao, Hardy Chan, A. DelaTorre, M. Fontelos, Mar'ia de Mar Gonz'alez, Juncheng Wei","doi":"10.4208/jms.v53n4.20.01","DOIUrl":"https://doi.org/10.4208/jms.v53n4.20.01","url":null,"abstract":"Non-local equations cannot be treated using classical ODE theorems. Nevertheless, several new methods have been introduced in the non-local gluing scheme of our previous article \"On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program\"; we survey and improve those, and present new applications as well. First, from the explicit symbol of the conformal fractional Laplacian, a variation of constants formula is obtained for fractional Hardy operators. We thus develop, in addition to a suitable extension in the spirit of Caffarelli--Silvestre, an equivalent formulation as an infinite system of second order constant coefficient ODEs. Classical ODE quantities like the Hamiltonian and Wronskian may then be utilized. As applications, we obtain a Frobenius theorem and establish new Pohovzaev identities. We also give a detailed proof for the non-degeneracy of the fast-decay singular solution of the fractional Lane-Emden equation.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43589044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
On Function Spaces with Mixed Norms — A Survey 关于混合范数的函数空间——综述
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2019-08-09 DOI: 10.4208/jms.v54n3.21.03
Long Huang, Dachun Yang
{"title":"On Function Spaces with Mixed Norms — A Survey","authors":"Long Huang, Dachun Yang","doi":"10.4208/jms.v54n3.21.03","DOIUrl":"https://doi.org/10.4208/jms.v54n3.21.03","url":null,"abstract":"The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is to provide a detailed proof for a useful inequality about mixed Lebesgue norms and the Hardy--Littlewood maximal operator and also to improve some known results on the maximal function characterizations of anisotropic mixed-norm Hardy spaces and the boundedness of Calder'on--Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct some errors and seal some gaps existing in the known articles.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 61
Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation 用算法微分法计算电磁整形中的形状导数
IF 0.8 4区 数学
Journal of Mathematical Study Pub Date : 2019-06-01 DOI: 10.4208/jms.v52n3.19.01
Karsten Eppler sci
{"title":"Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation","authors":"Karsten Eppler sci","doi":"10.4208/jms.v52n3.19.01","DOIUrl":"https://doi.org/10.4208/jms.v52n3.19.01","url":null,"abstract":"Shape optimization based on analytical shape derivatives is meanwhile a well-established tool in engineering applications. For an appropriate discretization of the underlying problem, the technique of algorithmic differentiation can also be used to provide a discrete analogue of the analytic shape derivative. The present article is concerned with the comparison of both types of gradient calculation and their effects on a gradient-based optimization method with respect to accuracy and performance, since so far only a few attempts have been made to compare these approaches. For this purpose, the article discusses both techniques and analyses the obtained numerical results for a generic test case from electromagnetic shaping. Since good agreement of both methods is found, algorithmic differentiation seems to be worthwhile to be used also for more demanding shape optimization problems. AMS subject classifications: 49M25, 49Q10, 78M15","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44035351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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