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A study of American option pricing for uncertain currency models with exponential O–U process 指数O-U过程下不确定货币模型的美式期权定价研究
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.cam.2025.117049
Lujun Zhou , Youfang Wang , Wei Wang , Xiaolan Yin
{"title":"A study of American option pricing for uncertain currency models with exponential O–U process","authors":"Lujun Zhou ,&nbsp;Youfang Wang ,&nbsp;Wei Wang ,&nbsp;Xiaolan Yin","doi":"10.1016/j.cam.2025.117049","DOIUrl":"10.1016/j.cam.2025.117049","url":null,"abstract":"<div><div>This paper prices American call and put options using a novel uncertain currency model. The model integrates the uncertain Vasicek interest rate term structure with the uncertain exponential Ornstein–Uhlenbeck exchange rate process, effectively capturing the dynamic changes in financial markets. Using the <span><math><mi>α</mi></math></span>-path method, the study derives pricing formulas for American call and put options. The model parameters are precisely estimated using the residual-based moment estimation method, and the robustness and applicability of the model are validated through goodness-of-fit tests. The results show that option prices are significantly dependent on parameters such as the initial exchange rate, interest rates, and strike price, and the model fits actual data well. This research not only provides a new theoretical basis for financial derivative pricing but also offers valuable insights for investors’ decision-making in uncertain market environments, holding significant academic and practical importance.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117049"},"PeriodicalIF":2.6,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
High-order multiscale hybridizable discontinuous Galerkin method for a class of one-dimensional oscillatory second-order equations 一类一维振荡二阶方程的高阶多尺度杂化不连续Galerkin方法
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.cam.2025.117047
Bo Dong , Wei Wang
{"title":"High-order multiscale hybridizable discontinuous Galerkin method for a class of one-dimensional oscillatory second-order equations","authors":"Bo Dong ,&nbsp;Wei Wang","doi":"10.1016/j.cam.2025.117047","DOIUrl":"10.1016/j.cam.2025.117047","url":null,"abstract":"<div><div>In this paper, we propose and analyze multiscale hybridizable discontinuous Galerkin (HDG) methods for solving a class of second-order equations with oscillatory solutions in one dimension. The high-order multiscale finite element spaces <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> contain non-polynomial basis functions that incorporate fine-scale features, as developed in our previous work (Dong and Wang, 2020). We prove that the resulting multiscale HDG method with the <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> space achieves optimal convergence in both the primary variable and its derivative with respect to the mesh size <span><math><mi>h</mi></math></span>, provided <span><math><mi>h</mi></math></span> is sufficiently small. Numerical experiments demonstrate that for both <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> spaces, the multiscale HDG methods exhibit second-order convergence without any resonance errors even when <span><math><mi>h</mi></math></span> is comparable to or larger than the wavelength scale, whereas the traditional HDG method with polynomial basis functions fails to converge in this regime. When <span><math><mi>h</mi></math></span> is smaller than the scale of the wavelength, numerical results confirm the optimal high-order convergence predicted by the error analysis. Our numerical results also demonstrate that the proposed methods are capable of capturing highly oscillating solutions of the Schrödinger equation in the application of the resonant tunneling diode (RTD) model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117047"},"PeriodicalIF":2.6,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A unified approach to high-order compact finite difference schemes for 3D Poisson equations 三维泊松方程高阶紧致有限差分格式的统一方法
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.cam.2025.117045
Kang Fu , Hongling Hu , Zhilin Li , Kejia Pan
{"title":"A unified approach to high-order compact finite difference schemes for 3D Poisson equations","authors":"Kang Fu ,&nbsp;Hongling Hu ,&nbsp;Zhilin Li ,&nbsp;Kejia Pan","doi":"10.1016/j.cam.2025.117045","DOIUrl":"10.1016/j.cam.2025.117045","url":null,"abstract":"<div><div>A unified approach to high-order compact finite difference schemes for solving three-dimensional Poisson equations is derived. Notice that all high order compact finite difference schemes are linear combinations of the solution values at grid points and source terms at selected points. In the unified strategy, a parameter <span><math><mi>γ</mi></math></span> is introduced for the linear combination of the solution values at the compact finite difference stencil. In our approach, carefully chosen <span><math><mi>γ</mi></math></span>’s lead to different fourth-order schemes. Carefully chosen linear combination of the source term at grid points will lead to different fourth-order schemes. If additional points such as the middle points are used, sixth-order schemes can be achieved if the solutions with certain symmetries. The convergence proof is provided for the new unified scheme based on the <span><math><mi>M</mi></math></span>-matrix condition along with non-trivial numerical examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117045"},"PeriodicalIF":2.6,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Solvability and iterative approximation of an infinite system of two-variable Hadamard-type fractional integral equations in ℓp space p空间中两变量hadamard型分数阶积分方程无穷系统的可解性与迭代逼近
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.cam.2025.117050
Sukanta Halder , Deepmala , Ravi P. Agarwal
{"title":"Solvability and iterative approximation of an infinite system of two-variable Hadamard-type fractional integral equations in ℓp space","authors":"Sukanta Halder ,&nbsp;Deepmala ,&nbsp;Ravi P. Agarwal","doi":"10.1016/j.cam.2025.117050","DOIUrl":"10.1016/j.cam.2025.117050","url":null,"abstract":"<div><div>In this paper, we examine an infinite system of two-variable functional integral equations involving Hadamard fractional integral operator. The analysis is carried out in the Banach sequence space <span><math><mrow><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>,</mo><mspace></mspace><mtext>for</mtext><mspace></mspace><mi>p</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. The primary objective of this study is to establish the existence of solutions based on certain assumptions using the Meir–Keeler condensing operator and the theory of measures of non-compactness. To support the theoretical results, we provide a concrete example. Furthermore, we construct an iterative algorithm by utilizing two semi-analytical methods-the modified homotopy perturbation method (abbreviated as MHPM) and Adomian’s decomposition method (abbreviated as ADM) to compute approximate solutions. A rigorous convergence analysis confirms that the sequence generated by the proposed algorithm converges in the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-norm. In addition, we perform a stability analysis to examine the sensitivity of the solution under initial data perturbations. Numerical results validate the theoretical findings and demonstrate the high accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117050"},"PeriodicalIF":2.6,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Exact non-parametric sequential convergence test for samplers 样本的精确非参数序列收敛检验
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.cam.2025.117051
Ivair R. Silva, Roger C.N. Ngassi, Gladston J.P. Moreira
{"title":"Exact non-parametric sequential convergence test for samplers","authors":"Ivair R. Silva,&nbsp;Roger C.N. Ngassi,&nbsp;Gladston J.P. Moreira","doi":"10.1016/j.cam.2025.117051","DOIUrl":"10.1016/j.cam.2025.117051","url":null,"abstract":"<div><div>Random number generators are extensively used in science. Generating pseudo-random numbers is the base for many data analysis techniques in computational statistics. This is the case, for instance, of most of the Bayesian methods, which are enabled by means of samplers such as the well-known Gibbs sampler and the Metropolis–Hastings. These classical Markov Chain Monte Carlo samplers are designed to generate a sequence of numbers that, under certain conditions, converge to a sequence that behaves as if sampled from a user-defined target distribution. In general, the number of iterations required to reach such convergence is not deterministic. There are several statistical tests for identifying that convergence has not yet been achieved, but not for actually signaling convergence. The present work introduces an exact non-parametric sequential test for signaling the convergence of random number generators in general. The solution is derived in the light of the type I error probability spending approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117051"},"PeriodicalIF":2.6,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Mixed-type multiple orthogonal Laurent polynomials on the unit circle 单位圆上的混合型多重正交洛朗多项式
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-06 DOI: 10.1016/j.cam.2025.117037
Edmundo J. Huertas , Manuel Mañas
{"title":"Mixed-type multiple orthogonal Laurent polynomials on the unit circle","authors":"Edmundo J. Huertas ,&nbsp;Manuel Mañas","doi":"10.1016/j.cam.2025.117037","DOIUrl":"10.1016/j.cam.2025.117037","url":null,"abstract":"<div><div>Mixed-type orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss–Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel–Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117037"},"PeriodicalIF":2.6,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Quasi-Newton L-BFGS based inexact primal–dual proximal point algorithms to solve nonsmooth convex composite programs for sparse signal recovery applications 基于准牛顿L-BFGS的非精确原对偶近点算法求解非光滑凸复合方案的稀疏信号恢复应用
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-09-02 DOI: 10.1016/j.cam.2025.117042
Yongchao Yu , Chongyang Wang
{"title":"Quasi-Newton L-BFGS based inexact primal–dual proximal point algorithms to solve nonsmooth convex composite programs for sparse signal recovery applications","authors":"Yongchao Yu ,&nbsp;Chongyang Wang","doi":"10.1016/j.cam.2025.117042","DOIUrl":"10.1016/j.cam.2025.117042","url":null,"abstract":"<div><div>In this work, we first propose a new inexact primal–dual proximal point algorithm (iPDPPA) for solving a general nonsmooth convex composite model with three focuses on the basis pursuit, the quadratically constrained <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-minimization and the Dantzig selector in the context of compressive sensing. We then prove its global convergence and discuss its convergence rate in some cases. We also prove that the objective function in the first subproblem of the proposed scheme is strongly convex and continuously differentiable, and then apply the quasi-Newton L-BFGS method to solve the subproblem. Numerical experiments show the effectiveness of L-BFGS-iPDPPA on sparse signal recovery.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117042"},"PeriodicalIF":2.6,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Delay-dependent stability conditions through the fundamental matrix of solutions for linear delay differential systems 线性时滞微分系统解的基本矩阵的时滞相关稳定性条件
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-08-31 DOI: 10.1016/j.cam.2025.117041
Guang-Da Hu
{"title":"Delay-dependent stability conditions through the fundamental matrix of solutions for linear delay differential systems","authors":"Guang-Da Hu","doi":"10.1016/j.cam.2025.117041","DOIUrl":"10.1016/j.cam.2025.117041","url":null,"abstract":"<div><div>We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the systems. Numerical examples illustrate the main results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117041"},"PeriodicalIF":2.6,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Anti-Gauss Laguerre polynomials: Some properties and a new interpolation process 反高斯拉盖尔多项式：一些性质和一种新的插值方法
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-08-30 DOI: 10.1016/j.cam.2025.117034
Luisa Fermo , Donatella Occorsio
{"title":"Anti-Gauss Laguerre polynomials: Some properties and a new interpolation process","authors":"Luisa Fermo ,&nbsp;Donatella Occorsio","doi":"10.1016/j.cam.2025.117034","DOIUrl":"10.1016/j.cam.2025.117034","url":null,"abstract":"<div><div>Anti-Gauss Laguerre quadrature formulas are based on the zeros of polynomials, we call them Anti-Gauss polynomials, defined in terms of Laguerre orthogonal polynomials. This paper establishes new properties of the Anti-Gauss Laguerre polynomials, and analyzes some “truncated” interpolation processes essentially based on their zeros. Estimates of the corresponding Lebesgue constants are proved, and error bounds in spaces of locally continuous functions, equipped with uniform weighted norms are given. Finally, some numerical tests are presented about the behavior of the Lebesgue functions and Lebesgue constants, and numerical experiments dealing with the approximation of functions having different smoothness are proposed. Comparisons with the results achieved by truncated Lagrange interpolation processes based on Laguerre zeros are shown.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117034"},"PeriodicalIF":2.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
An infeasible projection-type algorithm for finding nonnegative ground state solutions of nonlinear Schrödinger equations 求解非线性Schrödinger方程非负基态解的非可行投影型算法
IF 2.6 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-08-30 DOI: 10.1016/j.cam.2025.117040
Lubin Cui , Shujing Yang , Xiaojing Zhang , Xingdong Zhao , Jinyun Yuan , Qi Wang
{"title":"An infeasible projection-type algorithm for finding nonnegative ground state solutions of nonlinear Schrödinger equations","authors":"Lubin Cui ,&nbsp;Shujing Yang ,&nbsp;Xiaojing Zhang ,&nbsp;Xingdong Zhao ,&nbsp;Jinyun Yuan ,&nbsp;Qi Wang","doi":"10.1016/j.cam.2025.117040","DOIUrl":"10.1016/j.cam.2025.117040","url":null,"abstract":"<div><div>In this paper, a projected infeasible algorithm is proposed to compute the positive ground states of the nonlinear Schrödinger (NLS) equation, which can be regarded as an energy minimization problem with an orthogonal constraint. To further preserve the positivity of the ground states which is a necessary condition in some physical systems such as the non-rotating Bose–Einstein condensates, the saturable equation and the modified Gross–Pitaevskii equation, the projection is added to the infeasible method. The local Q-linearly convergence analysis of algorithm is established for the appropriate parameter values. Numerical experiments about computing the ground states of different types of the NLS equations illustrate that the proposed algorithm is efficient and faster than other feasible algorithms in dealing with large-scale problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"475 ","pages":"Article 117040"},"PeriodicalIF":2.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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