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A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods
Mir Md. Moheuddin,
Muhammad Abdus Sattar Titu,
Saddam Hossain
Issue:
Volume 9, Issue 3, June 2020
Pages:
46-54
Received:
4 May 2020
Accepted:
9 June 2020
Published:
20 June 2020
Abstract: In this paper, we mainly propose the approximate solutions to solve the integration problems numerically using the quadrature method including the Trapezoidal method, Simpson’s 1/3 method, and Simpson’s 3/8 method. The three proposed methods are quite workable and practically well suitable for solving integration problems. Through the MATLAB program, our numerical solutions are determined as well as compared with the exact values to verify the higher accuracy of the proposed methods. Some numerical examples have been utilized to give the accuracy rate and simple implementation of our methods. In this study, we have compared the performance of our solutions and the computational attempt of our proposed methods. Moreover, we explore and calculate the errors of the three proposed methods for the sake of showing our approximate solution’s superiority. Then, among these three methods, we analyzed the approximate errors to prove which method shows more appropriate results. We also demonstrated the approximate results and observed errors to give clear idea graphically. Therefore, from the analysis, we can point out that only the minimum error is in Simpson’s 1/3 method which will beneficial for the readers to understand the effectiveness in solving the several numerical integration problems.
Abstract: In this paper, we mainly propose the approximate solutions to solve the integration problems numerically using the quadrature method including the Trapezoidal method, Simpson’s 1/3 method, and Simpson’s 3/8 method. The three proposed methods are quite workable and practically well suitable for solving integration problems. Through the MATLAB progra...
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Investor’s Optimal Strategy with and Without Transaction Cost Under Ornstein-Uhlenbeck and Constant Elasticity of Variance (CEV) Models Via Exponential Utility Maximization
Silas Abahia Ihedioha,
Nanle Tanko Danat,
Audu Buba
Issue:
Volume 9, Issue 3, June 2020
Pages:
55-63
Received:
5 June 2020
Accepted:
20 June 2020
Published:
4 July 2020
Abstract: In this work, we studied the optimal investment problem of an investor who had exponential utility preference and traded two assets; (1) a risky asset which price dynamics was governed by the Constant Elasticity of variance (CEV) model and (2) a risk-free asset which price system followed the Ornstein-Uhlenbeck model. We employed the maximum principle of dynamic programming to obtain the Hamilton-Jacobi-Bellman (H-J-B) equation on which the first principle and the elimination of variable dependency were applied to get the closed-form of the investor’s optimal strategies. Two scenarios where the Brownian motions correlated and where they did not correlate were investigated. Also considered were the cases of when transaction cost was involved and when transaction cost was not involved. This lead to six cases that among the results obtained was that the investor has an optimal investment strategy that requires more amount of money for investment when the Brownian motions do not correlate and there is transaction cost than when the Brownian motions correlate and there is no transaction.
Abstract: In this work, we studied the optimal investment problem of an investor who had exponential utility preference and traded two assets; (1) a risky asset which price dynamics was governed by the Constant Elasticity of variance (CEV) model and (2) a risk-free asset which price system followed the Ornstein-Uhlenbeck model. We employed the maximum princi...
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Some Separate Quasi-Asymptotics Properties of Multidimensional Distributions and Application
Issue:
Volume 9, Issue 3, June 2020
Pages:
64-69
Received:
17 June 2020
Accepted:
3 July 2020
Published:
13 July 2020
Abstract: Quasi-asymptotic behavior of functions as a method has its application in observing many physical phenomena which are expressed by differential equations. The aim of the asymptotic method is to allow one to present the solution of a problem depending on the large (or small) parameter. One application of asymptotic methods in describing physical phenomena is the quasi-asymptotic approximation. The aim of this paper is to look at the quasi-asymptotic properties of multidimensional distributions by extracted variable. Distribution T(x0,x) from S'(Ṝ+1×Rn) has the property of the separability of variables, if it can be represented in form T(x0,x)=∑φi(x0)ψi (x) where distributions, φi(x0) from S'(Ṝ1) and ψi from S(Rn), x0 from Ṝ1+ and x is element Rn different values of do not depend on each other. Distribution T(x0,x) the element S'(Ṝ+1×Rn) is homogeneous and of order α at variable x0 is element Ṝ1+ and x=x1,x2,…,xn from Rn if for k>0 it applies that T(kx0,kx)=kα T(x0,x). The method of separating variables is one of the most widespread methods for solving linear differential equations in mathematical physics. In this paper, the results by V. S Vladimirov are used to present the proof of the basic theorems, regarding the quasi-asymptotic behavior of multidimensional distributions by a singular variable, with the application of quasi-asymptotics to the solution of differential equations.
Abstract: Quasi-asymptotic behavior of functions as a method has its application in observing many physical phenomena which are expressed by differential equations. The aim of the asymptotic method is to allow one to present the solution of a problem depending on the large (or small) parameter. One application of asymptotic methods in describing physical phe...
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