- I am a professor of mathematics (Ph.D) since 35 years at Ibn Tofail University, Faculty of sciences, department of ma... moreI am a professor of mathematics (Ph.D) since 35 years at Ibn Tofail University, Faculty of sciences, department of mathematics, Kénitra City , Morocco. I have original publications in maths, and I am a member of Amercain Mathematical Society. I reviewed 100 items from Mathematical Reviews and I am named one of sciensific leaders in maths of the world in 2016 from International Biographical Center, England, Cambridge.edit
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence... more
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of a solution of a game.
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We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence... more
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of a solution of a game.
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We study here stability properties of a class of well-posed optimization problems under suitable variational convergences. Moreover we investigate the stability for uniformly well-posed optimization problems. We give applications to... more
We study here stability properties of a class of well-posed optimization problems under suitable variational convergences. Moreover we investigate the stability for uniformly well-posed optimization problems. We give applications to mathematical programming
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This manuscript presents a simulation comparison of statistical classical methods and machine learning algorithms for time series forecasting notably the ARIMA model, K-Nearest Neighbors (KNN), The support Vector Regression (SVR), and... more
This manuscript presents a simulation comparison of statistical classical methods and machine learning algorithms for time series forecasting notably the ARIMA model, K-Nearest Neighbors (KNN), The support Vector Regression (SVR), and Long-Short Term Memory (LSTM). The performance of the models was evaluated using different metrics especially Mean Squared Error (MSE), Mean Absolute Error (MAE), Median Absolute Error (Median AE), and Root Mean Squared Error (RMSE). The results of the simulations approve that KNN algorithm has better accuracy than the others models’ forecasting notably in the middle and long terms. The MAPE for the KNN model was around 4.976843 while SVR and LSTM architectures had a MAPE of 6.810311 and 13.992133 respectively. In the medium and long term, ML models are so powerful on big datasets. Paradoxically, Machine learning architectures outperform ARIMA for shorter-term predictions. Thus, ARIMA is most appropriate in the case of univariate small data sets, where...
Economic and social change in a digital era is making the insurance ecosystem more complex. It makes several agents interact for different purposes. Therefore, a reflection on the insurance ecosystem modelling through multi-agent... more
Economic and social change in a digital era is making the insurance ecosystem more complex. It makes several agents interact for different purposes. Therefore, a reflection on the insurance ecosystem modelling through multi-agent simulation seems interesting since it allows to capture the complexity of today’s insured on the one hand and on the other hand to measure the solvency of insurance and reinsurance companies (EAR) in order to ensure the viability of the said ecosystem. Thus, this research aims at modeling the Moroccan insurance ecosystem within the framework of a new risk-based solvency directive for the case of loan death cover and on the basis of a set of exogenous and endogenous factors that influence the solvency of insurance and reinsurance companies in Morocco. This paper is carried out on the basis of a model, developed using NetLogo software, consisting of 4 agents that interact in the case of the “borrower’s death” guarantee, namely: the insured, the EAR, the banks and the Supervisory Authority of Insurance and Social Welfare (ACAPS). Each agent has a set of characteristics and seeks a defined objective. Thus, the modelling carried out allows testing the impact of endogenous and exogenous variables on the solvency of the EAR according to a simulation in three scenarios (central, rainy and risky).
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The Islamic finance sector has experienced significant development in several countries of the world and has shown resilience in the face of various crises, including the financial crisis of 2008. According to scientists, this sector has... more
The Islamic finance sector has experienced significant development in several countries of the world and has shown resilience in the face of various crises, including the financial crisis of 2008. According to scientists, this sector has the potential to grow significantly in the coming years. Takaful insurance plays a key role in this sector due to its dual economic and social vocation. Indeed, this activity involves several agents who help each other for different purposes while respecting Islamic principles. In this context, this work leads a reflection on a modelling of this sector by a multi-agent simulation. The latter allows us to deduce from the analysis of the micro-level behaviour of agents, the viability of the sector at the macro level. Indeed, this research models the ecosystem of the Moroccan Takaful insurance on the basis of a set of simulations aimed at measuring the impact of certain hypotheses on the viability of the sector. Also, the work was inspired by work done on the conventional insurance sector [1].The work was carried out on the basis of a Takaful Insurance and Reinsurance Company (EART) which manages a Takaful fund of the “Takaful Tamil” death guarantee of the Murabaha contract. The model assumes that the EART manages the fund on the basis of a Wakala contract and simulates the results under three scenarios relating to the technical and financial surplus distribution methods (prorata, selectivity and compensation).
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Research Interests: Mathematics and Pi
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ABSTRACT
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In this paper, we will combine random set theory and portfolio theory, through the estimation of the lower bound of the Markowitz random set based on the Mean-Variance Analysis of Asset Portfolios Approach, which represents the efficient... more
In this paper, we will combine random set theory and portfolio theory, through the estimation of the lower bound of the Markowitz random set based on the Mean-Variance Analysis of Asset Portfolios Approach, which represents the efficient frontier of a portfolio. There are several Markowitz optimization approaches, of which we denote the most known and used in the modern theory of portfolio, namely, the Markowitz’s approach, the Markowitz Sharpe’s approach and the Markowitz and Perold’s approach, generally these methods are based on the minimization of the variance of the return of a portfolio. On the other hand, the method used in this paper is completely different from those denoted above, because it is based on the theory of random sets, which allowed us to have the mathematical structure and the graphic of the Markowitz set. The graphical representation of the Markowitz set gives us an idea of the investment region. This region, called the investment zone, contains the stocks in which the rational investor can choose to invest. Mathematical and statistical estimation techniques are used in this paper to find the explicit form of the Markowitz random set, and to study its elements in function of the signs of the estimated parameters. Finally, we will apply the results found to the case of the returns of a portfolio composed of 200 assets from the Paris Stock Market Prices. The results obtained by this simulation allow us to have an idea on the stocks to recommend to the investors. In order to optimize their choices, these stocks are those which will be located above the curve of the hyperbola which represents the Markowitz set.
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There are many existing studies released in the field of Computer Vision, especially the field of Automatic License Plate Recognition. However, most of them are focused on using one method at the time, such as Thresholding algorithms,... more
There are many existing studies released in the field of Computer Vision, especially the field of Automatic License Plate Recognition. However, most of them are focused on using one method at the time, such as Thresholding algorithms, Edge Detections or Morphological transformations. This research paper proposes to automate the License plate recognition process, by combining four algorithms from the three methods mentioned above: Adaptive Thresholding, Otsu's Thresholding, Canny Edge Detection and Morphological Gradient applied to Edge Detection. The Goal achieved is to obtain the best binary image from those methods, and the statistical technique used in, is the median of pixel's intensity of all output images obtained by the four methods. Additionally, this research offers a comparative study on thresholding techniques to choose the best method for binarizing an image, which is the first and crucial step of Automatic License Plate Recognition Process.
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Writer Identification has gained increasing importance in the scientific community in recent years. In this paper, we propose an approach based on the combination of local textural descriptors and encoding methods (VLAD and Triangulation... more
Writer Identification has gained increasing importance in the scientific community in recent years. In this paper, we propose an approach based on the combination of local textural descriptors and encoding methods (VLAD and Triangulation Embedding). The tests carried out in the bilingual LAMIS dataset made it possible to reach 100% in the Arabic version and 100% in the French version.
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The digital revolution, the availability and the immediacy of information are the key factors that define today’s consumer. A demanding consumer who can easily judge value for money. As a result, the insurer is obliged to offer the... more
The digital revolution, the availability and the immediacy of information are the key factors that define today’s consumer. A demanding consumer who can easily judge value for money. As a result, the insurer is obliged to offer the correct rate for these insurance products. For this reason, the aim of this article is to give a basic pricing for the cover of the “disease” risk by the application of the generalized linear model and the proposal of an alternative pricing based on the Data Science.
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The ultimate objective of the problem under study is to apply the min-max tool, thus making it possible to optimize the default risks linked to several areas: the agricultural sector, for example, which requires the optimization of the... more
The ultimate objective of the problem under study is to apply the min-max tool, thus making it possible to optimize the default risks linked to several areas: the agricultural sector, for example, which requires the optimization of the default risk using the following elements: silage crops, annual consumption requirements, and crops produced for a given year. To minimize the default risk in the future, we start, in the first step, by forecasting the total budget of agriculture investment for the next 20 years, then distribute this budget efficiently between the irrigation and construction of silos. To do this, Bangladesh was chosen as an empirical case study given the availability of its data on the FAO website; it is considered a large agricultural country in South Asia. In this article, we give a detailed and original in-depth study of the agricultural planning model through a calculating algorithm suggested to be coded on the R software thereafter. Our approach is based on an or...
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We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence... more
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of a solution of a game.
Soit Φ : X −→ IR + un référentiel borné sur les bornés d'un espace de Banach X. Dans cet article, nous exprimons la convergence d'Attouch-Wets en terme de la convergence des approximations inf-convolutives de paramètres assez... more
Soit Φ : X −→ IR + un référentiel borné sur les bornés d'un espace de Banach X. Dans cet article, nous exprimons la convergence d'Attouch-Wets en terme de la convergence des approximations inf-convolutives de paramètres assez petits associéesassociéesà Φ. Plus précisément, nous montrons que la convergence d'Attouch-Wets d'une suite de fonctions de Γ (X) estéquivalenteestéquivalente d'une partàpartà la convergence dans le même sens des suites associées des approximations inf-convolutives de paramètres assez petits, et d'autre partàpartà la convergence uniforme sur les bornés de X de ces mêmes suites d'approximations. Dans le cas o` u Φ =. , nous retrouvons le théorème 4.3 de [9]; qui joue un rôle fondamental dans la démonstration de l'´ equivalence entre la convergence précédente et la semi-continuité inférieure uniforme sur les bornés d'un certain opérateur différentiel (voir [9]). Abstract Let Φ : X −→ IR + be a kernel bounded on bounded subsets of a Banach space X and f be a proper lower semicontinuous convex function defined on X. The inf-convolution approximates of f of parameters λ > 0 associated to Φ are the functions defined for each x ∈ X by f λ (x) := inf f (u) + Φ x−u λ : u ∈ X. In this article, we express the Attouch-Wets convergence of sequences in Γ (X) by the convergence of their associated sequences of c Math-Rech. & Appl. 2 D. Mentagui, K. El Hajioui inf-convolution approximates. More precisely, we prove that the Attouch-Wets convergence of sequences in Γ (X) is equivalent to the convergence in the same sense of their associated sequences of inf-convolution approximates of sufficiently small parameters, which is also equivalent to their uniform convergence on bounded subsets of X. If Φ = ., then we find the characterisation of the Attouch-Wets convergence in terms of the uniform convergence on bounded subsets of the Baire-Wijsman regularizations; which plays a key role in the characterisation of the previous convergence by the uniform lower semicontinuity on bounded subsets of a certain differentiel operator (see [9]).
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Let K+ be a kernel bounded on bounded subsets of a normed linear space X and / be a function in T(X). The inf-convolution approximates of / of parameters A > 0 associated to <£ are the functions defined for each x e X by f\(x) =... more
Let K+ be a kernel bounded on bounded subsets of a normed linear space X and / be a function in T(X). The inf-convolution approximates of / of parameters A > 0 associated to <£ are the functions defined for each x e X by f\(x) = inf{/(u) + (p1) : u G X}. In this article, we prove that the slice convergence of a sequence in T(X) is equivalent on the one hand to the convergence in the same sense of its sequences of infconvolution approximates of sufficiently small parameters associated to <£, and on the other hand to the pointwise convergence of the regularized sequences defined in the theorem 3.10 of this paper. As well, we show that the AttouchWets convergence of is equivalent to the convergence in the same sense of its approximate sequences when the parameters A converge to 0; which is also equivalent to their uniform convergence on bounded subsets of X. Then, we generalize in particular the main results of G. Beer [12] established in the case of Baire-Wijsman regularizati...
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This paper aims to introduce a large class of new general stabilization methods in optimization and saddle point theory. The concept of well-posedness in several senses is also investigated in metric and normed spaces. New variational... more
This paper aims to introduce a large class of new general stabilization methods in optimization and saddle point theory. The concept of well-posedness in several senses is also investigated in metric and normed spaces. New variational asymptotic methods and some variational approximation results have been displayed within the framework of variational analysis and the theory of variational convergence of functions and operators.
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In this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al... more
In this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al Horani, A. Yousef, M. Sababhehb [4].
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The study of kriging robustness has shown that, when the condition number of the covariance matrix is small, kriging is stable. Whereas when this number is too big kriging may be unstable with respect to perturbations of the covariance... more
The study of kriging robustness has shown that, when the condition number of the covariance matrix is small, kriging is stable. Whereas when this number is too big kriging may be unstable with respect to perturbations of the covariance function parameter. In this paper, we recall the use of the PLS regression in the estimation of a stationnary spatial field with known mean, which has positive and meaningful weights. Then we compare robustness of the PLS regression estimation to the kriging one when the range parameter is perturbed. We will see that when the covariance matrix is well conditioned, kriging of all the area from the same observations set, is done with the same stability level. However, the PLS regression estimate is always stable even when the condition number of the covariance matrix is too big.
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Dans cet article, nous introduisons la notion d'Attouch-Wetsépi Wetsépi/hypo-convergence des suites de fonctions convexes-concaves que nous caractérisons, d'abord en terme de Lagrangiens augmentés généralisés, puis en terme... more
Dans cet article, nous introduisons la notion d'Attouch-Wetsépi Wetsépi/hypo-convergence des suites de fonctions convexes-concaves que nous caractérisons, d'abord en terme de Lagrangiens augmentés généralisés, puis en terme d'approximations inf-sup-convolutives généralisées. Notre outil clé est le théorème principal (héorème 3.1) de notre référence [13]. Abstract In this article, we introduce the notion of the Attouch-Wets epi/hypo-convergence of sequences of convex-concave functions which we characterise, first in term of generalized augmented Lagrangians, then in term of generalized inf-sup-convolution approximates. Ours key tool is the main theorem (theorem 3.1) of ours reference [13].
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The yield curve is an essential tool in the evaluation and appreciation of the value of money over time. it plays a decisive role in the life of an insurance company and a pension organization. Indeed, it is a central tool for calculating... more
The yield curve is an essential tool in the evaluation and appreciation of the value of money over time. it plays a decisive role in the life of an insurance company and a pension organization. Indeed, it is a central tool for calculating and evaluating global commitment over a given time horizon.Today, Morocco is in the process of structuring these sectors, with the launch of a risk-based solvency project for the insurance sector and a bipolar systemic reform for the retirement sector. The implementation of these projects will lead to the unification of the different valuation and appraisal assumptions, including the risk-free interest rate curve.The purpose of this paper is to construct the Moroccan zero coupon yield curve based on the Smith-Wilson method.