Applied Mathematics and Modelling in Finance, Marketing and Economics (Studies in Computational Intelligence, 1114)

✍ Scribed by Said Melliani (editor), Oscar Castillo (editor), Abdelmajid El Hajaji (editor)

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 245
• Edition: 1
• Category: Library

✦ Synopsis

This book offers a comprehensive overview of the latest advancements in the field of applied mathematics as it relates to finance, marketing, and economics. It covers a range of topics including the effective utilization of applied mathematics and mathematical modeling in finance, economics, and marketing. Additionally, it explores the intersection between applied mathematics and practical applications in various scientific fields. The book targets a multidisciplinary audience, fostering the exchange of diverse ideas and showcasing the broad appeal of different subjects. It delves into recent developments in areas such as mathematical modeling in finance, mathematical modeling in marketing, the modeling of financial and economic fundamentals (e.g., interest rates, asset prices), market behavior modeling, modeling market imperfections, pricing financial derivative securities, hedging strategies, numerical methods, and financial engineering.

The book features selected contributions presented at the first edition of the International Conference in Applied Mathematics to Finance, Marketing and Economics, which took place at the National School of Commerce and Management in El Jadida, Morocco, from November 26 to 27, 2020.

✦ Table of Contents

Preface
Contents
High-Precision Method for Space-Time-Fractional Klein-Gordon Equation
1 Introduction
2 Description of the Fractional Calculus and Sine Method
2.1 Description of the Fractional Calculus
2.2 Description of Sine Method
3 Application
3.1 Conformable Space-Time-Fractional Klein-Gordon Equation with Cubic Nonlinearity
3.2 Implementation of Sine-Cosine Method
3.3 Two-Dimensional Space-Time Fractional Klein-Gordon Equations
3.4 Three-Dimensional Space-Time Fractional Klein-Gordon Equations
4 Numerical Examples and Discussion
5 Conclusion
References
Construction of a Bivariate C2 Septic Quasi-interpolant Using the Blossoming Approach
1 Introduction
2 Preliminaries
2.1 Polynomials on Triangles
2.2 Blossom of a Polynomial
3 The Blossom of a Spline
4 Construction of C2 Septic Quasi-interpolants
4.1 Construction Algorithm
4.2 Properties of the Quasi-Interpolation Operator
5 Numerical Examples
6 Conclusion
References
Solving Fuzzy Linear Programming Using the Parametric Form
1 Introduction
2 Preliminaries
3 Results and Discussion
4 Conclusion and Future Perspective
References
Dynamic and Static Simulated Annealing for Solving the Multi-objective k-Minimum Spanning Tree Problem
1 Introduction
2 Problem Formulation
3 Proposed Approaches
4 Numerical Experiments
5 Conclusion
References
Kantorovich Methods for Urysohn Integral Equations
1 Introduction
2 Preliminaries and Method
3 Convergence Rates
4 Discrete Methods
5 Numerical Results
References
The Maximal Numerical Range of a Quadratic Matrix
1 Introduction
2 Maximal Numerical Range of a Quadratic Matrix
References
The Effect of Change in Basilar Membrane Stiffness on the Micromechanics Cochlear Model
1 Introduction
2 Model of Cochlear Mechanics
3 Materials and Methods
3.1 Implementation of Cochlear Mechanics Model Using Finite Difference Method
3.2 Solution of the Coupled Equations Using Cramer's Rule
4 Results and Discussion
4.1 Response of Cochlear Partition Model
5 The Effect of BM Stiffness on the Displacement of the CP
6 Conclusion
7 Conflicts of Interest
References
New Variant of the GOST Digital Signature Protocol
1 Introduction
2 Review of Elliptic Curves Theory
2.1 Group Law
2.2 Multiplication of a Point by an Integer
2.3 The Discrete Logarithm Problem
3 GOST R 34.10-2012 Digital Signature Scheme ch8gost
3.1 Keys Production
3.2 The Signature Generation
3.3 Signature Verification
3.4 Signature Verification
4 Our Contribution
4.1 Keys Production
4.2 The Signature Equation
4.3 How Can Alice Generate a Signature
4.4 Signature Verification
4.5 Numerical Example
4.6 Security Analysis
4.7 Running Time
5 Conclusion
References
Existence and Uniqueness Solutions of Fuzzy Fractional Integration-Differential Problem Under Caputo gH-Differentiability
1 Introduction
2 Preliminaries
3 Main Results
4 Illustrations
5 Conclusions
References
Social Dilemmas and the Emergence of Cooperation in Financing Public Goods
1 Introduction
2 Social Dilemmas and Social Preference Models
2.1 The Role of Social Preferences
2.2 Social Preference Models
3 Social Preferences in Public-Good Games
3.1 The Public Goods Game
3.2 Towards Public-Good Games with Social Preferences Theories
4 Discussion
5 Conclusion
References
Fundamental Systems of Units of Some Imaginary Multiquadratic Fields of Degree 16
1 Introduction
2 Preliminary Results
3 Proof of the Main Theorem
References
One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method
1 Introduction
2 Mathematical Formulation
3 The Method of Fundamental Solution (MFS)
4 Numerical Results
5 Conclusion
References
Comparison Between Gradient Descent and Adam Algorithms for Image Reconstruction in Diffuse Optical Tomography
1 Introduction
2 Formulation of the Forward Problem
3 Inverse Problem
4 Numerical Results
5 Conclusion
References
Modelling and Forecasting Individuals Using the Internet (% of Population) in Morocco
1 Introduction
2 The Model and Its Probabilistic Characteristics
2.1 Analytical Representation of the Model
2.2 Distribution of the Process
3 Moments of the Process
4 Estimation of Parameters
4.1 Aspects on Optimization Methods
4.2 Estimated TF and Estimated CTF
5 Simulation
6 Application to Real-World Data
6.1 Comparing the Fitness of the Proposed Model and the Lognormal Model
7 Conclusion
References
A Comparative Study of Dam-Break Problem over a Sandy Bottom by an Unstructured Finite Volume Method
1 Introduction
2 Mathematical Model
3 Numerical Scheme
3.1 Finite Volume Roe-Scheme
3.2 Second Order Approximation in Space
3.3 Second Order Approximation in Time
3.4 Boundary Conditions
3.5 Treatment of the Source Term
3.6 Mesh Adaptation
4 Numerical Results
4.1 Test 1
4.2 Test 2
4.3 Test 3
5 Conclusion
References
Valuing a European Option Under the Heston Model with Interest Rate
1 Introduction
2 The Dynamics of the Heston-LS Model
3 Pricing Formula for European Options
4 Numerical Experiments
5 Appendix
6 Conclusion
References
A Multi-objective Approach to Energy Efficiency in Cellular Networks
1 Introduction
2 Related Work
3 System Model and Problem Formulation
3.1 Traffic State of the Mobile Users
3.2 Approach Proactive
3.3 Problem Modeling
4 Simulated Annealing Algorithm Solution
4.1 The Neighborhood of a Solution
4.2 SA Algorithm Solution
5 Simulation Results and Application
5.1 Description of Data
5.2 Computational Results
6 Conclusion
References
Inverse Problem of 2D Lung Electrical Impedance Tomography
1 Introduction
2 Mechanism of Operation
3 The Forward Problem
3.1 The Mathematical Model of the Forward Problem
4 The Inverse Problem
4.1 The Mathematical Model of Inverse Problem
4.2 The Numerical Simulations of Inverse Problem
5 Conclusion
References
On Local and Global Bisection-Type Mesh Refinements in C Programming Language
1 Introduction
2 Background
3 Mesh Generation
3.1 Mesh Data Structure
3.2 Rectangular and Triangular Mesh Generation of a Rectangle
4 Mesh Refinement
4.1 Global Refinement of a Rectangular, Triangular, and Mixed Meshes
4.2 Local Refinement of a Triangular Mesh
5 Refinement Algorithms
5.1 Algorithms for Global Refinement
5.2 Algorithms for Local Refinement
6 Conclusion
References