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AppliedMath
Volume 1
Issue 1
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AppliedMath, Volume 1, Issue 1 (December 2021) – 5 articles

Cover Story (view full-size image): Portfolio optimization models aid in the selection of financial assets by investors. As a result, when making financial decisions, portfolio management is critical. This paper defines and explores a time-varying tangency portfolio under nonlinear constraints (TV-TPNC) problem as a nonlinear programming (NLP) problem. Note that the most efficient portfolio in finance is the tangency portfolio, which is formed by the intersection point of the efficient frontier and the capital market line (CML). Since heuristics are widely used to solve NLP problems, a semi-integer beetle antennae search (SIBAS) algorithm is proposed to solve the TV-TPNC problem. The main results of numerical applications in real-world datasets demonstrate that our method is a splendid substitute for other evolutionary methods. View this paper
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11 pages, 439 KiB  
Article
Diversification of Time-Varying Tangency Portfolio under Nonlinear Constraints through Semi-Integer Beetle Antennae Search Algorithm
by Vasilios N. Katsikis and Spyridon D. Mourtas
AppliedMath 2021, 1(1), 63-73; https://doi.org/10.3390/appliedmath1010005 - 20 Dec 2021
Cited by 5 | Viewed by 2468
Abstract
In finance, the most efficient portfolio is the tangency portfolio, which is formed by the intersection point of the efficient frontier and the capital market line. This paper defines and explores a time-varying tangency portfolio under nonlinear constraints (TV-TPNC) problem as a nonlinear [...] Read more.
In finance, the most efficient portfolio is the tangency portfolio, which is formed by the intersection point of the efficient frontier and the capital market line. This paper defines and explores a time-varying tangency portfolio under nonlinear constraints (TV-TPNC) problem as a nonlinear programming (NLP) problem. Because meta-heuristics are commonly used to solve NLP problems, a semi-integer beetle antennae search (SIBAS) algorithm is proposed for solving cardinality constrained NLP problems and, hence, to solve the TV-TPNC problem. The main results of numerical applications in real-world datasets demonstrate that our method is a splendid substitute for other evolutionary methods. Full article
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26 pages, 11634 KiB  
Article
Aligned Magnetic Field and Radiation Effects on Biomagnetic Fluid over an Unsteady Stretching Sheet with Various Slip Conditions
by Anik Gomes, Jahangir Alam, Ghulam Murtaza, Tahmina Sultana, Efstratios E. Tzirtzilakis and Mohammad Ferdows
AppliedMath 2021, 1(1), 37-62; https://doi.org/10.3390/appliedmath1010004 - 14 Dec 2021
Cited by 1 | Viewed by 2622
Abstract
The aim of the present study is to analyze the effects of aligned magnetic field and radiation on biomagnetic fluid flow and heat transfer over an unsteady stretching sheet with various slip conditions. The magnetic field is assumed to be sufficiently strong enough [...] Read more.
The aim of the present study is to analyze the effects of aligned magnetic field and radiation on biomagnetic fluid flow and heat transfer over an unsteady stretching sheet with various slip conditions. The magnetic field is assumed to be sufficiently strong enough to saturate the ferrofluid, and the variation of magnetization is approximated by a linear function of temperature difference. The governing boundary layer equations with boundary conditions are simplified by suitable transformations. Numerical solution is obtained by using the bvp4c function technique in MATLAB software. The numerical results are derived for the velocity, temperature, the skin friction coefficient, and the rate of heat transfer. The evaluated results are compared with analytical study documented in scientific literature. The present investigation illustrates that the fluid velocity is decreased with the increasing values of radiation parameter, magnetic parameter, and ferromagnetic interaction parameter, though is increased as the Prandtl number, Grashof number, permeable parameter and thermal slip parameter are increased. In this investigation, the suction/injection parameter had a good impact on the skin friction coefficient and the rate of heat transfer. Full article
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19 pages, 507 KiB  
Article
Comparative Assessment of Hierarchical Clustering Methods for Grouping in Singular Spectrum Analysis
by Hossein Hassani, Mahdi Kalantari and Christina Beneki
AppliedMath 2021, 1(1), 18-36; https://doi.org/10.3390/appliedmath1010003 - 14 Dec 2021
Cited by 3 | Viewed by 2910
Abstract
Singular spectrum analysis (SSA) is a popular filtering and forecasting method that is used in a wide range of fields such as time series analysis and signal processing. A commonly used approach to identify the meaningful components of a time series in the [...] Read more.
Singular spectrum analysis (SSA) is a popular filtering and forecasting method that is used in a wide range of fields such as time series analysis and signal processing. A commonly used approach to identify the meaningful components of a time series in the grouping step of SSA is the utilization of the visual information of eigentriples. Another supplementary approach is that of employing an algorithm that performs clustering based on the dissimilarity matrix defined by weighted correlation between the components of a time series. The SSA literature search revealed that no investigation has compared the various clustering methods. The aim of this paper was to compare the effectiveness of different hierarchical clustering linkages to identify the appropriate groups in the grouping step of SSA. The comparison was performed based on the corrected Rand (CR) index as a comparison criterion that utilizes various simulated series. It was also demonstrated via two real-world time series how one can proceed, step-by-step, to conduct grouping in SSA using a hierarchical clustering method. This paper is supplemented with accompanying R codes. Full article
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15 pages, 630 KiB  
Article
On New Types of Multivariate Trigonometric Copulas
by Christophe Chesneau
AppliedMath 2021, 1(1), 3-17; https://doi.org/10.3390/appliedmath1010002 - 14 Dec 2021
Cited by 7 | Viewed by 2714
Abstract
Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While there is a plethora of copulas, those based on [...] Read more.
Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While there is a plethora of copulas, those based on trigonometric functions, especially in dimensions greater than two, have received much less attention. They are, however, of interest because of the properties of oscillation and periodicity of the trigonometric functions, which can appear in certain models of correlation of natural phenomena. In order to fill this gap, this paper introduces and investigates two new types of “multivariate trigonometric copulas”. Their main theoretical properties are studied, and some perspectives for applications are sketched for future work. In particular, we show that the proposed copulas are symmetric, not associative, with no orthant dependence, and with copula densities that have wide oscillations, which remains an uncommon property in the field. The expressions of their multivariate Spearman’s rho are also determined. Furthermore, the first type of the proposed copulas has the interesting feature of having a multivariate Spearman’s rho equal to 0 for all of the dimensions. Some graphic evidence supports the findings. Some mathematical formulas involving the product of n trigonometric functions may be of independent interest. Full article
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2 pages, 297 KiB  
Editorial
AppliedMath—Cultivating Profitable Frontier of Mathematics
by Takayuki Hibi
AppliedMath 2021, 1(1), 1-2; https://doi.org/10.3390/appliedmath1010001 - 7 Sep 2021
Viewed by 2782
Abstract
Mathematics has been built over thousands of years of history, since the creation of ancient civilizations [...] Full article
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