Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable
Jagdish Kumar Pahade,
Manoj Jha
Issue:
Volume 10, Issue 1, February 2021
Pages:
1-9
Received:
12 January 2021
Accepted:
19 January 2021
Published:
10 February 2021
Abstract: Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.
Abstract: Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fu...
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Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme
Siele Charles,
Rotich John,
Adicka Daniel
Issue:
Volume 10, Issue 1, February 2021
Pages:
10-18
Received:
18 January 2021
Accepted:
26 January 2021
Published:
12 March 2021
Abstract: The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t)and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.
Abstract: The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential e...
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About Exact Solution of Some Non Linear Partial Integro-differential Equations
Francis Bassono,
Rasmané Yaro,
Joseph Bonazebi Yindoula,
Gires Dimitri Nkaya,
Gabriel Bissanga
Issue:
Volume 10, Issue 1, February 2021
Pages:
19-29
Received:
15 January 2021
Accepted:
24 February 2021
Published:
30 March 2021
Abstract: Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.
Abstract: Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-diff...
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