Pub Date : 2023-06-01DOI: 10.4208/aam.oa-2022-0015
Qifeng Zhang null, Lu Zhang
{"title":"Linearly Compact Difference Scheme for the Two-Dimensional Kuramoto-Tsuzuki Equation with the Neumann Boundary Condition","authors":"Qifeng Zhang null, Lu Zhang","doi":"10.4208/aam.oa-2022-0015","DOIUrl":"https://doi.org/10.4208/aam.oa-2022-0015","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":"48790482","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}
Pub Date : 2023-06-01DOI: 10.4208/aam.oa-2023-0012
Lianfeng Liu
. 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.
． 在本文中，我们总结了基于Siu和Yang (Acta Math)提出的期权估值模型对指数期权的实际研究结果。达成。罪。心血管病。爵士。， 25(3) (2009)， pp. 339-388)，其中集成了EMM内核，该内核考虑了状态切换模型的所有风险组件。此外，使用隐马尔可夫状态切换模型对期权中经济的状态切换风险进行定价，其中风险标的资产由离散时间有限状态隐马尔可夫链调制，其状态代表经济的隐藏状态。我们根据2009年10月至2010年10月(即提出模型的年份)的真实金融数据，将该模型应用于恒生指数期权的定价。我们采用了Siu和Yang (Acta Math)提出的熵鞅测度(EMM)方法。达成。罪。心血管病。爵士。， 25(3) (2009)， pp. 339-388)来确定马尔可夫调制GBM的最优鞅测度。此外，我们提出了一种称为加权差分法的数值技术来补充EMM方法。我们还验证了我们最近提出的状态切换下的扩展跳跃扩散模型。j·菲南。Eng。， 6(4)(2019)， 1950038)，使用从上海证券交易所获得的50ETF期权，时间跨度为2018年1月至2022年12月。此外，我们还强调了基于EMM核的马尔可夫政权转换模型在现实世界中为价外指数期权定价的挑战。
{"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}
Pub Date : 2023-06-01DOI: 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}
Pub Date : 2023-05-01DOI: 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}
Pub Date : 2022-06-01DOI: 10.4208/aam.oa-2021-0090
Jiong Cai, Haixia Liu, Yang Wang
. 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.
{"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}
Pub Date : 2022-06-01DOI: 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}
Pub Date : 2022-06-01DOI: 10.4208/aam.oa-2021-0016
Hongzhi Tong, Michael Ng
. 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.
{"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}
Pub Date : 2022-06-01DOI: 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}
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