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Geometric Asian power option pricing with transaction cost under the geometric fractional Brownian motion with w sources of risk in fuzzy environment 模糊环境中具有 w 个风险源的几何分形布朗运动下带有交易成本的几何亚洲电力期权定价
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-24 DOI: 10.1016/j.cam.2024.116165
{"title":"Geometric Asian power option pricing with transaction cost under the geometric fractional Brownian motion with w sources of risk in fuzzy environment","authors":"","doi":"10.1016/j.cam.2024.116165","DOIUrl":"10.1016/j.cam.2024.116165","url":null,"abstract":"<div><p>In this paper, we obtain an explicit formula to calculate the geometric Asian power option price with floating strike price and transaction cost under the fractional geometric Brownian motion model with w sources of risk and fuzzy parameters. First, by considering the Leland and Kabanov theorems, we derive a non-linear PDE with the transaction cost formula to obtain the option price. Then, using the Green function find a closed form solution for the PDE and achieve the price of the option under different amounts of the model and option parameters. Next, we consider the model’s parameters as fuzzy numbers and acquire a general formula to obtain intervals for the option price under different belief degrees and power option parameter amounts.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141838687","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
Bounds for the distribution and moments of the forward and backward recurrence times in a renewal process 更新过程中前向和后向递推时间的分布和矩的边界
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-24 DOI: 10.1016/j.cam.2024.116166
{"title":"Bounds for the distribution and moments of the forward and backward recurrence times in a renewal process","authors":"","doi":"10.1016/j.cam.2024.116166","DOIUrl":"10.1016/j.cam.2024.116166","url":null,"abstract":"<div><p>We obtain a variety of lower and upper bounds for the bivariate tail of the joint distribution between the (forward and backward) recurrence times in a renewal process. Some of these bounds are valid generally, some others in the case where the interarrival distribution <span><math><mi>F</mi></math></span> exhibits monotone aging. We also give various bounds for the moments of the recurrence times. Our results improve upon existing bounds for these quantities in the literature. We also discuss the case where the aging of <span><math><mi>F</mi></math></span> is non-monotonic. Finally, we present numerical examples to illustrate the performance of the new bounds.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141848291","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 arbitrary Lagrangian–Eulerian positivity-preserving finite volume scheme for radiation hydrodynamics equations in the equilibrium-diffusion limit 平衡扩散极限辐射流体力学方程的任意拉格朗日-欧勒正保有限体积方案
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116156
{"title":"An arbitrary Lagrangian–Eulerian positivity-preserving finite volume scheme for radiation hydrodynamics equations in the equilibrium-diffusion limit","authors":"","doi":"10.1016/j.cam.2024.116156","DOIUrl":"10.1016/j.cam.2024.116156","url":null,"abstract":"<div><p>In this paper, an arbitrary Lagrangian–Eulerian (ALE) positivity-preserving finite volume scheme is constructed for radiation hydrodynamics equations (RHE) in the equilibrium-diffusion limit. Firstly, the integral form equations of RHE in the ALE framework are presented. Then, the operator-splitting method is applied to divide the equations into hyperbolic part and parabolic part. In addition, a second-order positivity-preserving finite volume scheme is constructed for the hyperbolic part based on MUSCL reconstruction. The vertex velocity is obtained by the predictor–corrector strategy. The Winslow method is applied to improve the quality of the Lagrangian mesh. Furthermore, a nonlinear positivity-preserving finite volume scheme suitable for distorted mesh is proposed for the parabolic part. Finally, some numerical examples are given to show the accuracy and reliability of the numerical scheme.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141842464","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
Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media 断裂和异质介质中时间分数热弹性问题的多尺度模型缩减
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116157
{"title":"Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media","authors":"","doi":"10.1016/j.cam.2024.116157","DOIUrl":"10.1016/j.cam.2024.116157","url":null,"abstract":"<div><p>In this paper, we consider the time fractional thermoporoelasticity problem in fractured and heterogeneous media. The mathematical model with a time memory formalism is described by a coupled system of equations for pressure, temperature and displacements. We use an implicit finite difference approximation for temporal discretization. We present a fine grid approximation based on the finite element method and Discrete Fracture Model (DFM) for two-dimensional model problems. Further, we use the Generalized Multiscale Finite Element Method (GMsFEM) for coarse grid approximation. The primary concept behind the proposed method is to streamline the complexity inherent in the thermoporoelasticity problem. Given that our model equation incorporates multiple fractional powers, leading to multiple unknowns with memory effects, we aim to address this intricacy by optimizing the problem’s dimensionality. As a result, the solution is sought on a coarse grid, a strategic choice that not only simplifies the computational cost but also contributes to significant time savings. We present numerical results for the two-dimensional model problems in heterogeneous fractured porous media. We derive relative errors between the reference fine grid solution and the multiscale solution for different numbers of multiscale basis functions. The results confirm that the proposed method is able to achieve good accuracy with a few degrees of freedoms on the coarse grid.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141840207","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 discontinuous Galerkin method for the Brinkman–Darcy-transport problem 布林克曼-达西传输问题的非连续伽勒金方法
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116155
{"title":"A discontinuous Galerkin method for the Brinkman–Darcy-transport problem","authors":"","doi":"10.1016/j.cam.2024.116155","DOIUrl":"10.1016/j.cam.2024.116155","url":null,"abstract":"<div><p>In this paper, a weighted discontinuous Galerkin finite element method and an upwind format are presented to solve the coupled Brinkman–Darcy flow and transport model. The flow in a highly permeable region of the model is governed by the Brinkman equations, and the percolation in the porous media is controlled by the Darcy equations, which are coupled by three interface conditions. The permeability coefficients in this model are strongly nonhomogeneous, anisotropic, and discontinuous; the transport equation is a convection-dominated problem; and the velocity field in the porous media domain does not satisfy the divergence-free condition. A weighted discontinuous Galerkin finite element method is used to solve the complex permeability coefficient problem and an upwind scheme is used to solve the convection dominated problem. The interface conditions can be naturally incorporated into the discrete formulation without introducing additional variables. Optimal error estimates are obtained for the semi-discretization and the full discretization with the backward Euler scheme in suitable energy norm. A series of numerical experiments are provided to illustrate the proposed method, including testing the convergence and accuracy of various types of meshes; simulating fluid flow in complex porous media such as obstacles, layered media, and curved interfaces; and studying the coupled flow behavior of surface-subsurface flows with contaminant transport.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141852965","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
Spectral approximation and error analysis for the transmission eigenvalue problem with an isotropic inhomogeneous medium 各向同性非均质介质传输特征值问题的频谱近似和误差分析
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116163
{"title":"Spectral approximation and error analysis for the transmission eigenvalue problem with an isotropic inhomogeneous medium","authors":"","doi":"10.1016/j.cam.2024.116163","DOIUrl":"10.1016/j.cam.2024.116163","url":null,"abstract":"<div><p>In this paper, we propose an effective Legendre-Fourier spectral method for the transmission eigenvalue problem in polar geometry with an isotropic inhomogeneous medium. The basic idea of this methodology is to rewrite the initial problem into its equivalent form by using polar coordinates and some specially designed polar conditions. A variational method and its discrete version (i.e., Legendre-Fourier spectral method) are then presented within a class of weighted Sobolev spaces. With the help of the spectral theory of compact operators and the approximation properties of some specially designed projections in non-uniformly weighted Sobolev spaces, error estimates with spectral accuracy of the Legendre-Fourier spectral method for both the eigenvalue and eigenfunction approximations are established. Numerical experiments are presented to confirm the theoretical findings and the efficiency of our algorithm.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141850183","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
Second-order numerical method for a neutral Volterra integro-differential equation 中性 Volterra 积分微分方程的二阶数值方法
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116160
{"title":"Second-order numerical method for a neutral Volterra integro-differential equation","authors":"","doi":"10.1016/j.cam.2024.116160","DOIUrl":"10.1016/j.cam.2024.116160","url":null,"abstract":"<div><p>This paper is dedicated to obtaining an approximate solution for a neutral second-order Volterra integro-differential equation. Our method is the second-order accurate finite difference scheme on a uniform mesh. The error analysis is carried out and numerical results are given to support the proposed approach.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141845372","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
Efficient exponential Rosenbrock methods till order four 直到四阶的高效指数罗森布洛克方法
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1016/j.cam.2024.116158
{"title":"Efficient exponential Rosenbrock methods till order four","authors":"","doi":"10.1016/j.cam.2024.116158","DOIUrl":"10.1016/j.cam.2024.116158","url":null,"abstract":"<div><p>In a previous paper, a technique was described to avoid order reduction with exponential Rosenbrock methods when integrating initial boundary value problems with time-dependent boundary conditions. That requires to calculate some information on the boundary from the given data. In the present paper we prove that, under some assumptions on the coefficients of the method which are mainly always satisfied, no numerical differentiation is required to approximate that information in order to achieve order 4 for parabolic problems with Dirichlet boundary conditions. With Robin/Neumann ones, just numerical differentiation in time may be necessary for order 4, but none for order <span><math><mrow><mo>≤</mo><mn>3</mn></mrow></math></span>.</p><p>Furthermore, as with this technique it is not necessary to impose any stiff order conditions, in search of efficiency, we recommend some methods of classical orders 2, 3 and 4 and we give some comparisons with several methods in the literature, with the corresponding stiff order.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0377042724004072/pdfft?md5=8949791707da4e1a1fc108adf49d7214&pid=1-s2.0-S0377042724004072-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141847855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the approximation to fractional calculus operators with multivariate Mittag-Leffler function in the kernel 关于内核为多元米塔格-勒夫勒函数的分数微积分算子近似值
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1016/j.cam.2024.116148
{"title":"On the approximation to fractional calculus operators with multivariate Mittag-Leffler function in the kernel","authors":"","doi":"10.1016/j.cam.2024.116148","DOIUrl":"10.1016/j.cam.2024.116148","url":null,"abstract":"<div><p>Several numerical techniques have been developed to approximate Riemann–Liouville (R - L) and Caputo fractional calculus operators. Recently linear positive operators have been started to use to approximate fractional calculus operators such as R - L, Caputo, Prabhakar and operators containing bivariate Mittag-Leffler functions. In the present paper, we first define and investigate the fractional calculus properties of Caputo derivative operator containing the multivariate Mittag-Leffler function in the kernel. Then we introduce approximating operators by using the modified Kantorovich operators for the approximation to fractional integral and Caputo derivative operators with multivariate Mittag-Leffler function in the kernel. We study the convergence properties of the operators and compute the degree of approximation by means of modulus of continuity and Hölder continuous functions. The obtained results corresponds to a large family of fractional calculus operators including R- L, Caputo and Prabhakar models.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141853901","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
Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses 带脉冲的离散时随机系统的几乎确定的指数稳定性和随机稳定性
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1016/j.cam.2024.116152
{"title":"Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses","authors":"","doi":"10.1016/j.cam.2024.116152","DOIUrl":"10.1016/j.cam.2024.116152","url":null,"abstract":"<div><p>This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141839079","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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