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Linearly Compact Difference Scheme for the Two-Dimensional Kuramoto-Tsuzuki Equation with the Neumann Boundary Condition 具有Neumann边界条件的二维Kuramoto-Tsuzuki方程的线性紧致差分格式
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2022-0015
Qifeng Zhang null, Lu Zhang
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引用次数: 0
Empirical Study on Option Pricing under Markov Regime Switching Economics 马尔可夫制度转换经济学下期权定价的实证研究
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0012
Lianfeng Liu
{"title":"Empirical Study on Option Pricing under Markov Regime Switching Economics","authors":"Lianfeng Liu","doi":"10.4208/aam.oa-2023-0012","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0012","url":null,"abstract":". In this research, we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang (Acta Math. Appl. Sin. Engl. Ser., 25(3) (2009), pp. 339–388), where an EMM kernel is integrated which takes into account all risk components of a regime-switching model. Further, the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We apply such a model to the pricing of Hang Seng Index options based on the real-world financial data from October 2009 to October 2010 (i.e., for the year in which the model was proposed). We employed the entropy martingale measure (EMM) approach proposed by Siu and Yang (Acta Math. Appl. Sin. Engl. Ser., 25(3) (2009), pp. 339–388) to determine the optimal martingale measure for the Markov-modulated GBM. In addition, we have proposed a numerical technique called the weighted difference method to compliment the EMM approach. We have also verified the extended jump-diffusion model under regime-switching that we proposed recently (Int. J. Finan. Eng., 6(4) (2019), 1950038) using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December 2022. Further, we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46611931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Mathematical Study for the Stability of Two Predator and One Prey with Infection in First Predator using Fuzzy Impulsive Control 一类捕食者感染下双捕食者和单捕食者稳定性的模糊脉冲控制数学研究
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0003
Khushbu Singh null, K. Kaladhar
{"title":"A Mathematical Study for the Stability of Two Predator and One Prey with Infection in First Predator using Fuzzy Impulsive Control","authors":"Khushbu Singh null, K. Kaladhar","doi":"10.4208/aam.oa-2023-0003","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0003","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44853789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Random Double Tensors Integrals 随机二重张量积分
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0004
Shih Yu Chang null, Yimin Wei
{"title":"Random Double Tensors Integrals","authors":"Shih Yu Chang null, Yimin Wei","doi":"10.4208/aam.oa-2023-0004","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0004","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43035172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media 层状介质中三维拉普拉斯方程的多极和局部展开的指数收敛理论
应用数学年刊:英文版 Pub Date : 2023-05-01 DOI: 10.4208/aam.oa-2023-0005
Wenzhong Zhang, Bo Cai
{"title":"Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media","authors":"Wenzhong Zhang, Bo Cai","doi":"10.4208/aam.oa-2023-0005","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0005","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46944949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gradient Descent for Symmetric Tensor Decomposition 对称张量分解的梯度下降
应用数学年刊:英文版 Pub Date : 2022-06-01 DOI: 10.4208/aam.oa-2021-0090
Jiong Cai, Haixia Liu, Yang Wang
{"title":"Gradient Descent for Symmetric Tensor Decomposition","authors":"Jiong Cai, Haixia Liu, Yang Wang","doi":"10.4208/aam.oa-2021-0090","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0090","url":null,"abstract":". Symmetric tensor decomposition is of great importance in applications. Several studies have employed a greedy approach, where the main idea is to (cid:12)rst (cid:12)nd a best rank-one approximation of a given tensor, and then repeat the process to the residual tensor by subtracting the rank-one component. In this paper, we focus on (cid:12)nding a best rank-one approximation of a given orthogonally order-3 symmetric tensor. We give a geometric landscape analysis of a nonconvex optimization for the best rank-one approximation of orthogonally symmetric tensors. We show that any local minimizer must be a factor in this orthogonally symmetric tensor decomposition, and any other critical points are linear combinations of the factors. Then, we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem, and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable tensors. This result, combined with the landscape analysis, reveals that the greedy algorithm will get the tensor CP low-rank decomposition. Numerical results are provided to verify our theoretical results.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41556383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion 调和分数布朗运动驱动的脉冲中立型随机泛函微分方程的全局吸引性和拟不变集
应用数学年刊:英文版 Pub Date : 2022-06-01 DOI: 10.4208/aam.oa-2021-0082
Y. Peng, Zhiang Li null, Liping Xu
{"title":"Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion","authors":"Y. Peng, Zhiang Li null, Liping Xu","doi":"10.4208/aam.oa-2021-0082","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0082","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49285312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Application of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and Beyond 乘法器交替方向法在约束抛物型最优控制问题中的应用
应用数学年刊:英文版 Pub Date : 2022-06-01 DOI: 10.4208/aam.oa-2022-0004
R. Glowinski, Yongcun Song, Xiaoming Yuan null, Hangrui Yue
{"title":"Application of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and Beyond","authors":"R. Glowinski, Yongcun Song, Xiaoming Yuan null, Hangrui Yue","doi":"10.4208/aam.oa-2022-0004","DOIUrl":"https://doi.org/10.4208/aam.oa-2022-0004","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48796249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces 再生核Hilbert空间中函数线性回归的梯度迭代方法
应用数学年刊:英文版 Pub Date : 2022-06-01 DOI: 10.4208/aam.oa-2021-0016
Hongzhi Tong, Michael Ng
{"title":"A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces","authors":"Hongzhi Tong, Michael Ng","doi":"10.4208/aam.oa-2021-0016","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0016","url":null,"abstract":". We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces. In the algorithm, we use an early stopping technique, instead of the classical Tikhonov regularization, to prevent the iteration from an overfitting function. Under mild conditions, we obtain upper bounds, essentially matching the known minimax lower bounds, for excess prediction risk. An almost sure convergence is also established for the proposed algorithm.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42703770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis and FDTD Simulation of a Perfectly Matched Layer for the Drude Metamaterial Drude超材料完全匹配层的分析与FDTD仿真
应用数学年刊:英文版 Pub Date : 2022-06-01 DOI: 10.4208/aam.oa-2022-0002
Jichun Li null, Li Zhu
{"title":"Analysis and FDTD Simulation of a Perfectly Matched Layer for the Drude Metamaterial","authors":"Jichun Li null, Li Zhu","doi":"10.4208/aam.oa-2022-0002","DOIUrl":"https://doi.org/10.4208/aam.oa-2022-0002","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46568592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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