aziz arbai | Université Abdelmalek Essaâdi (original) (raw)

Papers by aziz arbai

On this paper we present a solution to detect and know if a point M is inside a polygon (A k) k∈{... more On this paper we present a solution to detect and know if a point M is inside a polygon (A k) k∈{1,...,n} or outside. In the case where the point M is at outside the polygon, a simple optimization method will be applied to determine the distance between the point M and the polygon A 1 , ..., An, that is to say between the point M and the point P of the border of the polygon closest to M : The Neighboring Point. The introduction of complex numbers in algebra and geometry is very useful. We therefore proceed with our purely geometric methods as well as with complex numbers, using the triangulation of a convex polygon and a very specific complex application that we have just constructed. So our contributions are: A very simple and fast tracking algorithm, and therefore an extremely low cost per iteration (An Algorithm for Judging Points Inside or Outside a Polygon), The neighboring Point and The spacing in the case where the point M is at outside the polygon, so without going through the quadratic optimization, we will give the simplest and fastest way to calculate the distance d between the point M and the polygon (Am) m∈{1,...,n} and determine the point P of the boundary of the closest (neighboring) polygon to M. Above all it is an article full of examples for all the cases and methods and which are ready to be programmed and applied.

viXra, Jul 1, 2020

In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, ... more In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, which is very important and useful especially when we cannot write the complex number a+ib in the exponential or the geometric form. And, we will propose a precise direct method and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy and resolve fastly all type of equations of the second degree .

viXra, Jul 1, 2020

Nous proposons la démonstration de l'hypothèse de Riemann, ainsi nous exposons une in…nité de nom... more Nous proposons la démonstration de l'hypothèse de Riemann, ainsi nous exposons une in…nité de nombres complexes (1/2) + ic qui sont les zéros (ayant pour partie réelle 1/2) de la fonction Zêta de Riemann, qui va aussi donnez la distribution et l'emplacement des nombres premiers. Mots-clés: Nombres complexes, fonction Zeta de Riemann,

International Journal of Technology Enhancements and Emerging Engineering Research, Jan 25, 2015

Markov chains are a method among methods we can use to describe the dynamics of a disease in its ... more Markov chains are a method among methods we can use to describe the dynamics of a disease in its different stages. While the theory and practice of modeling of Markov chains Epidemiology is not new, rather the basic application of this powerful tool can be used by nonmathematicians as well. In this work, we present the above theory by announcing the assumptions and conditions of use of Markov chains in the study of diseases and specifically breast cancer, which could facilitate the formulation of hypotheses, and understanding the evolution of the disease in a population. We focus on absorbing Markov chains in discrete time, and we are going step by step to calculate the probability of infection with breast cancer for an individual, the duration of each state and the life expectancy for infected people. These quantities are useful for characterizing the dynamics of a disease and can help researchers to explore key aspects of the evolution of the disease into a population.

International Journal of Applied Mathematics, Apr 22, 2017

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

IOSR journal of mathematics, May 1, 2017

Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particu... more Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particular parameter useful in characterizing the fine structure of several type of stochastic process whether the data are free or include diffusion component and whether the process contains indefinite activities and finite/in finite variation. In this paper, we summarize theoretical searcher work; this provides a CGMY-FT closed form solution algorithm for pricing option. For accuracy and validation we implement our method to price European call options and compare the results to a numerical simulation.

International Journal of Applied Mathematics, Jun 30, 2021

In this paper, we propose a new study of the Black and Scholes Process (BSP). The main objective ... more In this paper, we propose a new study of the Black and Scholes Process (BSP). The main objective is to add a threshold parameter to the Black and Scholes Process. Using Kolmogorov equations, we obtain the probability density function and the moments of the process. Estimators of the parameters are studied by considering discrete sampling of the sample trajectories of the model and then using the maximum likelihood method and the Wicksell method.

Abstract—blackThis article we propose a log normal distribution with a threshold parameter. This ... more Abstract—blackThis article we propose a log normal distribution with a threshold parameter. This was considered as an extension of the bi-parameter process by adding third parameter. The Kolmogorov equations and Ito’s stochastic differential equations give us the transition probability density function and the moments of this process. Assuming the discrete sampling of the sample path of the model, the local maximum-likelihood estimate the parameters except the threshold, which it estimation requires us to solve a non-linear equation for this, Newton-Raphson method is called. Index Terms—blackThree-parameter; log normal process; discrete sampling; diffusion process; local maximum-likelihood estimation. I.

International Journal of Technology Enhancements and Emerging Engineering Research, 2015

Markov chains are a method among methods we can use to describe the dynamics of a disease in its ... more Markov chains are a method among methods we can use to describe the dynamics of a disease in its different stages. While the theory and practice of modeling of Markov chains Epidemiology is not new, rather the basic application of this powerful tool can be used by nonmathematicians as well. In this work, we present the above theory by announcing the assumptions and conditions of use of Markov chains in the study of diseases and specifically breast cancer, which could facilitate the formulation of hypotheses, and understanding the evolution of the disease in a population. We focus on absorbing Markov chains in discrete time, and we are going step by step to calculate the probability of infection with breast cancer for an individual, the duration of each state and the life expectancy for infected people. These quantities are useful for characterizing the dynamics of a disease and can help researchers to explore key aspects of the evolution of the disease into a population.

viXra, 2020

We propose the demonstration of the Riemann hypothesis, thus we explicitly expose (an infinity of... more We propose the demonstration of the Riemann hypothesis, thus we explicitly expose (an infinity of complex numbers α=(1/2)+ic ) the zeros (having for real part 1/2) of the Zeta function of Riemann, which will also give exactly the distribution and location of the prime numbers.

International Journal of Apllied Mathematics, 2017

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

IOSR Journal of Mathematics, 2017

Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particu... more Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particular parameter useful in characterizing the fine structure of several type of stochastic process whether the data are free or include diffusion component and whether the process contains indefinite activities and finite/in finite variation. In this paper, we summarize theoretical searcher work; this provides a CGMY-FT closed form solution algorithm for pricing option. For accuracy and validation we implement our method to price European call options and compare the results to a numerical simulation.

European Scientific Journal, Jul 12, 2013

This works deals with the teaching and learning of mathematics in Moroccan universities. Our Goal... more This works deals with the teaching and learning of mathematics in Moroccan universities. Our Goal is to better understand difficulties encountered by students, with math, and to study in which measure the integration of new technologies of information and communication may help them overcome these difficulties, by favoring interactions between representation by ICT and classical representation of the concerned course. On the basis of the instrumental approach of computers in teaching, we start from the hypothesis that succeeding to this type of mathematical tasks requires, beyond knowing adequate commands and their syntax, learning specific instrumented techniques, in a context taken in charge by the institution. In our thesis, a technique to represent called 3D technology occupies a central part, as a means to reduce the distance between the knowledge teachable and the knowledge to be taught. The works includes an institutional analysis (ecological analysis of university curriculum) about the teaching of mathematics and the use of 3D technology, as well as two experiments, without and with the other.

viXra, 2020

In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, ... more In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, which is very important and useful especially when we cannot write the complex number a+ib in the exponential or the geometric form. And, we will propose a precise direct method and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy and resolve fastly all type of equations of the second degree .

With the advent of interactive media, learning by playing is taking a variety of forms. Serious g... more With the advent of interactive media, learning by playing is taking a variety of forms. Serious game, this term may seem contradictory, in reality it reflexes a very current reality, it rests on the video culture playful learners. This type of games is appropriate for investing in classrooms, the idea is to make learning more interactive and motivating. They have been developed to enable learners to build their own knowledge, skills and knowhow to develop highlevel skills to deal with complex situations. In this paper, we present the concept of serious game, and our educational software who contain the attractive exercises and a serious game for mathematics.We design this softwarein Arabic to make mental calculation appreciate to novicestudents. And we believe that this type of software can be used to increasestudents'motivation to learn, and their interest in mental calculation.

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

In this paper, we will see some alternative estimation methods for the multidimensional lognormal... more In this paper, we will see some alternative estimation methods for the multidimensional lognormal distribution three-parametric (and for the three-parameter lognormal difusion process) as the method of maximum likelihood, the median method, the method of the straight of Wicksell and two different method of the maximum of likelihood amended. In the case of estimation: the method of moments and the estimation of maximum likelihood revised.

In this paper we will propose a direct method which is accurate and fast to solve the equations o... more In this paper we will propose a direct method which is accurate and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy. Finaly we found also the general formula that gives us the second roots (square root) of a complex number.

In this paper we will propose a direct method which is accurate and fast to solve the equations o... more In this paper we will propose a direct method which is accurate and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy. And finaly also we found the general formula that gives us the second roots (square root) of a complex number.

On this paper we present a solution to detect and know if a point M is inside a polygon (A k) k∈{... more On this paper we present a solution to detect and know if a point M is inside a polygon (A k) k∈{1,...,n} or outside. In the case where the point M is at outside the polygon, a simple optimization method will be applied to determine the distance between the point M and the polygon A 1 , ..., An, that is to say between the point M and the point P of the border of the polygon closest to M : The Neighboring Point. The introduction of complex numbers in algebra and geometry is very useful. We therefore proceed with our purely geometric methods as well as with complex numbers, using the triangulation of a convex polygon and a very specific complex application that we have just constructed. So our contributions are: A very simple and fast tracking algorithm, and therefore an extremely low cost per iteration (An Algorithm for Judging Points Inside or Outside a Polygon), The neighboring Point and The spacing in the case where the point M is at outside the polygon, so without going through the quadratic optimization, we will give the simplest and fastest way to calculate the distance d between the point M and the polygon (Am) m∈{1,...,n} and determine the point P of the boundary of the closest (neighboring) polygon to M. Above all it is an article full of examples for all the cases and methods and which are ready to be programmed and applied.

viXra, Jul 1, 2020

In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, ... more In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, which is very important and useful especially when we cannot write the complex number a+ib in the exponential or the geometric form. And, we will propose a precise direct method and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy and resolve fastly all type of equations of the second degree .

viXra, Jul 1, 2020

Nous proposons la démonstration de l'hypothèse de Riemann, ainsi nous exposons une in…nité de nom... more Nous proposons la démonstration de l'hypothèse de Riemann, ainsi nous exposons une in…nité de nombres complexes (1/2) + ic qui sont les zéros (ayant pour partie réelle 1/2) de la fonction Zêta de Riemann, qui va aussi donnez la distribution et l'emplacement des nombres premiers. Mots-clés: Nombres complexes, fonction Zeta de Riemann,

International Journal of Technology Enhancements and Emerging Engineering Research, Jan 25, 2015

Markov chains are a method among methods we can use to describe the dynamics of a disease in its ... more Markov chains are a method among methods we can use to describe the dynamics of a disease in its different stages. While the theory and practice of modeling of Markov chains Epidemiology is not new, rather the basic application of this powerful tool can be used by nonmathematicians as well. In this work, we present the above theory by announcing the assumptions and conditions of use of Markov chains in the study of diseases and specifically breast cancer, which could facilitate the formulation of hypotheses, and understanding the evolution of the disease in a population. We focus on absorbing Markov chains in discrete time, and we are going step by step to calculate the probability of infection with breast cancer for an individual, the duration of each state and the life expectancy for infected people. These quantities are useful for characterizing the dynamics of a disease and can help researchers to explore key aspects of the evolution of the disease into a population.

International Journal of Applied Mathematics, Apr 22, 2017

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

IOSR journal of mathematics, May 1, 2017

Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particu... more Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particular parameter useful in characterizing the fine structure of several type of stochastic process whether the data are free or include diffusion component and whether the process contains indefinite activities and finite/in finite variation. In this paper, we summarize theoretical searcher work; this provides a CGMY-FT closed form solution algorithm for pricing option. For accuracy and validation we implement our method to price European call options and compare the results to a numerical simulation.

International Journal of Applied Mathematics, Jun 30, 2021

In this paper, we propose a new study of the Black and Scholes Process (BSP). The main objective ... more In this paper, we propose a new study of the Black and Scholes Process (BSP). The main objective is to add a threshold parameter to the Black and Scholes Process. Using Kolmogorov equations, we obtain the probability density function and the moments of the process. Estimators of the parameters are studied by considering discrete sampling of the sample trajectories of the model and then using the maximum likelihood method and the Wicksell method.

Abstract—blackThis article we propose a log normal distribution with a threshold parameter. This ... more Abstract—blackThis article we propose a log normal distribution with a threshold parameter. This was considered as an extension of the bi-parameter process by adding third parameter. The Kolmogorov equations and Ito’s stochastic differential equations give us the transition probability density function and the moments of this process. Assuming the discrete sampling of the sample path of the model, the local maximum-likelihood estimate the parameters except the threshold, which it estimation requires us to solve a non-linear equation for this, Newton-Raphson method is called. Index Terms—blackThree-parameter; log normal process; discrete sampling; diffusion process; local maximum-likelihood estimation. I.

International Journal of Technology Enhancements and Emerging Engineering Research, 2015

Markov chains are a method among methods we can use to describe the dynamics of a disease in its ... more Markov chains are a method among methods we can use to describe the dynamics of a disease in its different stages. While the theory and practice of modeling of Markov chains Epidemiology is not new, rather the basic application of this powerful tool can be used by nonmathematicians as well. In this work, we present the above theory by announcing the assumptions and conditions of use of Markov chains in the study of diseases and specifically breast cancer, which could facilitate the formulation of hypotheses, and understanding the evolution of the disease in a population. We focus on absorbing Markov chains in discrete time, and we are going step by step to calculate the probability of infection with breast cancer for an individual, the duration of each state and the life expectancy for infected people. These quantities are useful for characterizing the dynamics of a disease and can help researchers to explore key aspects of the evolution of the disease into a population.

viXra, 2020

We propose the demonstration of the Riemann hypothesis, thus we explicitly expose (an infinity of... more We propose the demonstration of the Riemann hypothesis, thus we explicitly expose (an infinity of complex numbers α=(1/2)+ic ) the zeros (having for real part 1/2) of the Zeta function of Riemann, which will also give exactly the distribution and location of the prime numbers.

International Journal of Apllied Mathematics, 2017

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

IOSR Journal of Mathematics, 2017

Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particu... more Empirical investigation of return dynamics leads searchers to introduce CGMY model with a particular parameter useful in characterizing the fine structure of several type of stochastic process whether the data are free or include diffusion component and whether the process contains indefinite activities and finite/in finite variation. In this paper, we summarize theoretical searcher work; this provides a CGMY-FT closed form solution algorithm for pricing option. For accuracy and validation we implement our method to price European call options and compare the results to a numerical simulation.

European Scientific Journal, Jul 12, 2013

This works deals with the teaching and learning of mathematics in Moroccan universities. Our Goal... more This works deals with the teaching and learning of mathematics in Moroccan universities. Our Goal is to better understand difficulties encountered by students, with math, and to study in which measure the integration of new technologies of information and communication may help them overcome these difficulties, by favoring interactions between representation by ICT and classical representation of the concerned course. On the basis of the instrumental approach of computers in teaching, we start from the hypothesis that succeeding to this type of mathematical tasks requires, beyond knowing adequate commands and their syntax, learning specific instrumented techniques, in a context taken in charge by the institution. In our thesis, a technique to represent called 3D technology occupies a central part, as a means to reduce the distance between the knowledge teachable and the knowledge to be taught. The works includes an institutional analysis (ecological analysis of university curriculum) about the teaching of mathematics and the use of 3D technology, as well as two experiments, without and with the other.

viXra, 2020

In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, ... more In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, which is very important and useful especially when we cannot write the complex number a+ib in the exponential or the geometric form. And, we will propose a precise direct method and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy and resolve fastly all type of equations of the second degree .

With the advent of interactive media, learning by playing is taking a variety of forms. Serious g... more With the advent of interactive media, learning by playing is taking a variety of forms. Serious game, this term may seem contradictory, in reality it reflexes a very current reality, it rests on the video culture playful learners. This type of games is appropriate for investing in classrooms, the idea is to make learning more interactive and motivating. They have been developed to enable learners to build their own knowledge, skills and knowhow to develop highlevel skills to deal with complex situations. In this paper, we present the concept of serious game, and our educational software who contain the attractive exercises and a serious game for mathematics.We design this softwarein Arabic to make mental calculation appreciate to novicestudents. And we believe that this type of software can be used to increasestudents'motivation to learn, and their interest in mental calculation.

Through this paper, we introduce Fourier transform as an alternative approach to pricing option w... more Through this paper, we introduce Fourier transform as an alternative approach to pricing option when the underlying asset follows Stochastic Volatility double Jump model (SVJJ). In fact the weakness of the traditional approaches does not depend on closed formula of probability density function which is explicitly unknown under this model. The advantage of Fourier transform technique is that for a wide class of stock price the only thing necessary to evaluate European call is a so called characteristic function since there is one-to-one relationship between a p.d.f & ch.f and both of which uniquely determine a probability distribution. For accuracy and validation we implement pricing formulas FFT, Monte Carlo simulation and we compare both of them to the benchmark model BS.

In this paper, we will see some alternative estimation methods for the multidimensional lognormal... more In this paper, we will see some alternative estimation methods for the multidimensional lognormal distribution three-parametric (and for the three-parameter lognormal difusion process) as the method of maximum likelihood, the median method, the method of the straight of Wicksell and two different method of the maximum of likelihood amended. In the case of estimation: the method of moments and the estimation of maximum likelihood revised.

In this paper we will propose a direct method which is accurate and fast to solve the equations o... more In this paper we will propose a direct method which is accurate and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy. Finaly we found also the general formula that gives us the second roots (square root) of a complex number.

In this paper we will propose a direct method which is accurate and fast to solve the equations o... more In this paper we will propose a direct method which is accurate and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy. And finaly also we found the general formula that gives us the second roots (square root) of a complex number.