Publication Date: 2007
Applied Mathematics and Computation (963003)189(1)pp. 341-345
In this paper, an application of homotopy perturbation method is applied to solve the nonlinear two-dimensional wave equation. The analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components. The non-homogenous equation is effectively solved by employing the phenomena of the self-canceling "noise" terms, where sum of components vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. Its remarkable accuracy properties are finally demonstrated by an example. © 2006 Elsevier Inc. All rights reserved.
Publication Date: 2007
International Journal of Computer Mathematics (10290265)84(1)pp. 75-79
In this paper we propose new ideas for the implementation of the Adomian decomposition method to solve nonlinear Volterra integral equations. Numerical examples are presented to illustrate the method for nonlinear Volterra integral equations of the second kind.
Publication Date: 2024
Journal Of The Iranian Statistical Society (17264057)23(1)pp. 99-115
This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits. © (2024), (Iranian Statistical Society). All rights reserved.
Publication Date: 2019
Communications in Statistics - Theory and Methods (1532415X)48(14)pp. 3464-3481
Recently, Lee and Cha proposed two general classes of discrete bivariate distributions. They have discussed some general properties and some specific cases of their proposed distributions. In this paper we have considered one model, namely bivariate discrete Weibull distribution, which has not been considered in the literature yet. The proposed bivariate discrete Weibull distribution is a discrete analogue of the Marshall–Olkin bivariate Weibull distribution. We study various properties of the proposed distribution and discuss its interesting physical interpretations. The proposed model has four parameters, and because of that it is a very flexible distribution. The maximum likelihood estimators of the parameters cannot be obtained in closed forms, and we have proposed a very efficient nested EM algorithm which works quite well for discrete data. We have also proposed augmented Gibbs sampling procedure to compute Bayes estimates of the unknown parameters based on a very flexible set of priors. Two data sets have been analyzed to show how the proposed model and the method work in practice. We will see that the performances are quite satisfactory. Finally, we conclude the paper. © 2018, © 2018 Taylor & Francis Group, LLC.
Publication Date: 2019
Sequential Analysis (07474946)38(3)pp. 279-300
In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated. © 2019, © 2019 Taylor & Francis Group, LLC.
Publication Date: 2018
Journal of Statistical Theory and Practice (15598616)12(3)pp. 595-614
In 1997, Marshall and Olkin introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions that brings more flexibility to the model. They demonstrated their method for the exponential and Weibull classes. In the same paper they briefly indicated its bivariate extension. The main aim of this article is to introduce the same method, for the first time, to the class of discrete generalized exponential distributions both for the univariate and bivariate cases. We investigate several properties of the proposed univariate and bivariate classes. The univariate class has three parameters, whereas the bivariate class has five parameters. It is observed that depending on the parameter values, the univariate class can be zero inflated as well as heavy tailed. We propose to use an expectation–maximization (EM) algorithm to estimate the unknown parameters. Small simulation experiments have been performed to see the effectiveness of the proposed EM algorithm, and a bivariate data set has been analyzed; it is observed that the proposed models and the EM algorithm work quite well in practice. © 2018, © 2018 Grace Scientific Publishing, LLC.
Publication Date: 2017
Statistics (02331888)51(5)pp. 1143-1158
In this paper, we develop a bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram [Discrete generalized exponential distribution of a second type. Statistics. 2013;47:876–887]. It is observed that the proposed bivariate distribution is a very flexible distribution and the bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution. J Multivariate Anal. 2009;100:581–593]. We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum-likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of one data set has been performed to show the effectiveness of the proposed model. Finally, we propose some open problems and conclude the paper. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2013
Communications in Statistics - Theory and Methods (1532415X)42(13)pp. 2324-2334
Skew-symmetric distributions of various types have been the center of attraction by many researchers in the literature. In this article, we will introduce a uni/bimodal generalization of the Azzalini's skew-normal distribution which is indeed an extension of the skew-generalized normal distribution obtained by Arellano-Valle et al. (2004). Our new distribution contains more parameters and thus it is more flexible in data modeling. Indeed, certain univariate case of the so called flexible skew-symmetric distribution of Ma and Genton (2004) is also a particular case of our proposed model. We will first study some basic distributional properties of the new extension, such as its distribution function, limiting behavior and moments. Then, we will investigate some useful results regarding its relation with other known distributions, such as student's t and skew-Cauchy distributions. In addition, we will present certain methods to generate the new distribution and, finally, we shall apply the model to a real data set to illustrate its behavior comparing to some rival models. © Taylor and Francis Group, LLC.
Publication Date: 2012
Statistical Papers (09325026)53(3)pp. 685-696
Skew-symmetric distributions of various types have been the center of attraction by many researchers in the literature. In this article, we shall introduce another more general class of skew distributions, specially related to the Laplace distribution. This new class contains some previously known skew distributions. We shall investigate different characteristics of members of this class such as its moments, thus generalizing a result of Umbach (Stat Probab Lett 76:507-512, 2006), limiting behavior, moment generating function, unimodality and reveal its natural occurrence as the distribution of some order statistics. In addition, we will generalize a result of Aryal and Rao (Nonlinear Anal 63:639-646, 2005) in connection with truncated skew-Laplace distribution and study its certain stochastic orderings. Some illustrative examples are also provided. © 2011 Springer-Verlag.
Publication Date: 2023
Kyoto Journal of Mathematics (21543321)63(4)pp. 829-849
Let C be a locally bounded k-category, where k is a field.We prove that C is pure-semisimple, that is, every object of Mod-C is pure-projective if and only if every family of morphisms between indecomposable finitely generated C-modules is Noetherian. Our formalism establishes the pure-semisimplicity of Galois coverings, that is, if C is a G-category with a free G-action on ind-C, then C is pure-semisimple if and only if C/G is so. © 2023 by Kyoto University.
Publication Date: 2016
Forum Mathematicum (09337741)28(2)pp. 377-389
We describe explicitly the Auslander-Reiten translation in the category of bounded complexes of finitely generated maximal Cohen-Macaulay modules, Cb(CM R), over a commutative local Cohen-Macaulay ring R with a canonical module ω. Then the Auslander-Reiten formula is generalized for complexes in Cb(CM R) and we prove the existence theorem of Auslander-Reiten sequences. As an application of our results, we investigate the existence of Auslander-Reiten triangles in the category of perfect complexes as a full triangulated subcategory of Db(mod R). © 2016 by De Gruyter 2016.
Publication Date: 2015
Journal of Algebra and its Applications (17936829)14(3)
Let λ be an artin algebra. By letting the Nakayama functor act degree-wise, we define a translation ? in the category of complexes of finitely generated λ-modules, C(mod λ). Then we investigate the existence of almost split sequences in the category C(mod λ). As an application of our results, we see that the full subcategory of D(mod λ) consisting of complexes isomorphic to perfect complexes admits almost split sequences. © World Scientific Publishing Company.
Publication Date: 2024
Journal Of Mathematics And Modeling In Finance (27830578)4(1)pp. 19-35
This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy. © 2024, Allameh Tabataba'i University. All rights reserved.
Publication Date: 2023
Computational Methods For Differential Equations (23453982)11(2)pp. 281-290
A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method. © 2023 University of Tabriz. All rights reserved.
Publication Date: 2018
Journal of Computational and Applied Mathematics (03770427)328pp. 252-266
One of the most important subject in financial mathematics is the option pricing. The most famous result in this area is Black–Scholes formula for pricing European options. This paper is concerned with a method for solving a generalized Black–Scholes equation in a reproducing kernel Hilbert space. Subsequently, the convergence of the proposed method is studied under some hypotheses which provide the theoretical basis of the proposed method. Furthermore, the error estimates for obtained approximation in reproducing kernel Hilbert space are presented. Finally, a numerical example is considered to illustrate the computation efficiency and accuracy of the proposed method. © 2017 Elsevier B.V.
Publication Date: 2015
CMES - Computer Modeling in Engineering and Sciences (15261492)109(3)pp. 247-262
In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for single- and two-asset options are illustrated. Copyright © 2015 Tech Science Press.
Publication Date: 2014
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics (12237027)76(1)pp. 51-58
In this paper, we consider an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We use the continuous linear Legendre multi-wavelets on the interval [0, 1) to solve this equation. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Tavassoli kajani m., ,
Vahdati, S.,
Abbas, Z.,
Maleki, M. Publication Date: 2012
Journal Of Applied Mathematics (16870042)2012
Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method. © 2012 M. Tavassoli Kajani et al.
Publication Date: 2010
Australian Journal of Basic and Applied Sciences (19918178)4(9)pp. 4193-4199
In this paper,We use the continuous Legendre multi-wavelets on the interval [0, 1) to solve Fredholm integral equations of the second kind. To do so, we reduced the solution of Fredholm integral equation to the solution of algebraic equations. Illustrative examples are included to show the high accuracy of the estimation, and to demonstrate validity and applicability of the technique. © 2010, INSInet Publication.
Publication Date: 2009
Applied Mathematical Sciences (discontinued) (1312885X)3(13-16)pp. 693-700
We use the continuous Legendre multi-wavelets on the interval [0,1) to solve the linear integro-differential equation. To do so, we reduced the problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Comparison has been done with two other methods and it shows that the accuracy of these results are higher than them.
Abbas, Z.,
Vahdati, S.,
Tavassoli kajani m., ,
Atan k.a., Publication Date: 2009
Applied Mathematics and Computation (18735649)210(2)pp. 473-478
In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a, b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions. © 2009 Elsevier Inc. All rights reserved.
Publication Date: 2007
AIP Conference Proceedings (0094243X)971pp. 105-111
In this paper we extend the 2-D directed graphical representation for DNA sequences. The main purpose is to making a directed graph corresponding to a DNA sequence which hasn't any complete coincidence of the edges. To prevent repetition of the edge e we define e→1 by using the outer product of two vectors and some mathematical concepts. Moreover, we have applied this method for some DNA sequences to show the advantage of this method over the some other methods. © 2008 American Institute of Physics.
Publication Date: 2025
Journal of Mathematical Modeling (2345394X)13(3)pp. 485-496
Asset prices typically follow significant trends influenced by the economic environment or overall investor sentiment. Regime-switching is commonly employed to capture asset price dynamics, as it effectively describes significant trends and reflects the changing correlations of asset returns over various periods. This paper explores multi-period mean-variance portfolio optimization under regime-switching with path-dependent returns. Unlike conventional models, this paper assumes that asset returns depend on the entire path of market states rather than just the current one. Consequently, investors base their decisions on all observed states up to the current moment. Utilizing dynamic programming techniques, we derive the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in closed form. Furthermore, we demonstrate that the results from the traditional regime-switching model, can be viewed as specific cases of our proposed model. © 2025 University of Guilan.
Publication Date: 2025
International Journal of Mathematics in Operational Research (17575850)30(3)pp. 392-414
In a financial market, the state of the underlying economy and investors’ mood affect market trends and consequently asset prices movements. Regime-switching models are used to describe changes in market states and trends. The main assumption in regime-switching models is that asset returns depend on the current state of the market. We generalise this assumption to the case where market states in the past, as well as the current state, affect asset returns. In fact, we assume that asset returns are market path-dependent. Under this assumption, we study a multi-period mean-variance portfolio selection problem in a Markovian regime-switching market when the time horizon is uncertain. Using the stochastic dynamic programming approach, we obtain the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in a closed form. We show that the results obtained under conventional regime-switching model, can be obtained as special cases of the present model. Copyright © 2025 Inderscience Enterprises Ltd.
Publication Date: 2024
OPSEARCH (00303887)
Market conditions profoundly influence investors’ decisions regarding market participation and exit strategies. This paper investigates the multi-period mean-variance portfolio selection problem within a regime-switching market framework, where the time horizon is uncertain and the exit time depends on observed market states. Although the exit time is market path-dependent, we do not regard it as a stopping time with respect to the market state filtration, and we also include exogenous stochastic factors in its determination. The Lagrangian duality method and dynamic programming are utilized to derive the analytical expressions for the optimal investment strategy and the mean-variance efficient frontier. A path-dependent version of the Bellman equation is derived, demonstrating that, at any given time, both the value function and the optimal portfolio are path-dependent. This is different from the standard regime-switching model, where they depend on the current state of the market at that time. Our framework encompasses models with current state-dependent exit times as a special case. This study provides a detailed case study analyzing the effectiveness of the exit mechanism and its implications on investment returns under different market scenarios. © The Author(s), under exclusive licence to Operational Research Society of India 2024.
Publication Date: 2024
Journal of the Operations Research Society of China (21946698)
This paper considers the Markowitz’s mean–variance portfolio selection model in a multi-period setting with regime switching and uncertain time horizon. The returns of the assets depend on the state of the market modulated by a discrete-time Markov chain with a finite state space. The exit time from the market is a stopping time with respect to the market state filtration. So, the definitive decision to exit the market at any time depends only on the market states up to that time. The original problem with uncertain exit time is reformulated as a problem with certain exit time. The Lagrange duality method and the dynamic programming approach are used to derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier. Toward this objective, a market path-dependent value function method is introduced and it is shown that optimal portfolios are market path dependent. The two cases where the exit time is the first hitting time to a specified subset of the market state space and the market state contains a bankruptcy state are investigated separately. Moreover, it is shown that some results in the existing literature can be obtained as special cases of the results in this paper. Finally, some numerical examples are presented to illustrate the results. © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2024.
