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Processus matriciels : simulation et modélisation de la dépendance en financeAhdida, Abdelkoddousse 01 December 2011 (has links)
La première partie de cette thèse est consacrée à la simulation des équations différentielles stochastiques définies sur le cône des matrices symétriques positives. Nous présentons de nouveaux schémas de discrétisation d'ordre élevé pour ce type d'équations différentielles stochastiques, et étudions leur convergence faible. Nous nous intéressons tout particulièrement au processus de Wishart, souvent utilisé en modélisation financière. Pour ce processus nous proposons à la fois un schéma exact en loi et des discrétisations d'ordre élevé. A ce jour, cette méthode est la seule qui soit utilisable quels que soient les paramètres intervenant dans la définition de ces modèles. Nous montrons, par ailleurs, comment on peut réduire la complexité algorithmique de ces méthodes et nous vérifions les résultats théoriques sur des implémentations numériques. Dans la deuxième partie, nous nous intéressons à des processus à valeurs dans l'espace des matrices de corrélation. Nous proposons une nouvelle classe d'équations différentielles stochastiques définies dans cet espace. Ce modèle peut être considéré comme une extension du modèle Wright-Fisher (ou processus Jacobi) àl'espace des matrice de corrélation. Nous étudions l'existence faible et forte des solutions. Puis, nous explicitons les liens avec les processus de Wishart et les processus de Wright-Fisher multi-allèles. Nous démontrons le caractère ergodique du modèle et donnons des représentations de Girsanov susceptibles d'être employées en finance. En vue d'une utilisation pratique, nous explicitons deux schémas de discrétisation d'ordre élevé. Cette partie se conclut par des résultats numériques illustrant le comportement de la convergence de ces schémas. La dernière partie de cette thèse est consacrée à l'utilisation des ces processus pour des questions de modélisation multi-dimensionnelle en finance. Une question importante de modélisation, aujourd'hui encore difficile à traiter, est l'identification d'un type de modèle permettant de calibrer à la fois le marché des options sur un indice et sur ses composants. Nous proposons, ici, deux types de modèles : l'un à corrélation locale et l'autre à corrélation stochastique. Dans ces deux cas, nous expliquons quelle procédure on doit adopter pour obtenir une bonne calibration des données de marché / After a short introduction (in French) to the multi dimensional modelling for index pricing problems, the first part of the thesis treats the simulation of stochastic differential equations defined on the cone of symmetric positive semi-definite matrices. Indeed, we present several second order discretization schemes associated to a general class of affine processes defined on $posm.$ We study also their weak convergence. We pay a special attention to Wishart processes, which are considered as a particular case of this class and have been frequently used in finance. In this case, we give an exact scheme and a third order discretization one. To the best of our knowledge, this is the first exact sampling of the Wishart distribution without any restrictions on its parameters. Some algorithm are proposed in order to enhance all scheme in term of computation of time. We show numerical illustrations of our convergence and compare it to the theoretical rate. We then focus on other type of processes defined on the correlation matrix space. For this purposes, We propose a new stochastic differential equation defined on $crr.$ We prove the weak and the strong existence of such solutions. These processes are considered as the extension of Wright-Fisher processes (or Jacobi process) on correlation matrices. We shed light on a useful connection with Wishart processes and Wright-Fisher multi-allèles. Moreover, we explicitly present their moments, which enable us to describe the ergodic limit. Other results about Girsanov representations are also given. Finally, in order to use these processes in practice, we propose second order discretization schemes based on two different methods. Numerical experiments are presented to show the convergence. The last part is devoted to multi dimension modelling in finance for baskets and indices pricing. After giving a mathematical analysis of models defined either by the correlation matrix or in the positive semi-definite semi positive one, we ask if we find the adequate structure of correlation models which is able to calibrate both the index options market and the single options market related to each component of this index. For this purpose, we propose two types of modelling, the first uses a local model correlation and the second derives from a pure stochastic correlation model. Moreover, we explain different routines that have been used for improved calibration
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Combining Business Intelligence, Indicators, and the User Requirements Notation for Performance MonitoringJohari Shirazi, Iman 26 November 2012 (has links)
Organizations use Business Intelligence (BI) systems to monitor how well they are meeting
their goals and objectives. Yet, very often BI systems do not include clear models of
the organization’s goals or of how to measure whether they are satisfied or not. Several
researchers now attempt to integrate goal models into BI systems, but there are still major
challenges related to how to get access to the BI data to populate the part of the goal
model (often indicators) used to assess goal satisfaction.
This thesis explores a new approach to integrate BI systems with goal models. In
particular, it explores the integration of IBM Cognos Business Intelligence, a leading BI
tool, with an Eclipse-based goal modeling tool named jUCMNav. jUCMNav is an open
source graphical editor for the User Requirements Notation (URN), which includes the
Use Case Map notation for scenarios and processes and the Goal-oriented Requirement
Language for business objectives. URN was recently extended with the concept of Key
Performance Indicator (KPI) to enable performance assessment and monitoring of business
processes. In jUCMNav, KPIs are currently calculated or modified manually. The
new integration proposed in this thesis maps these KPIs to report elements that are generated
automatically by Cognos based on the model defined in jUCMNav at runtime, with
minimum effort. We are using IBM Cognos Mashup Service, which includes web services
that enable the retrieval of report elements at the most granular level. This transformation
provides managers and analysts with useful goal-oriented and process-oriented
monitoring views fed by just-in-time BI information. This new solution also automates
retrieving data from Cognos servers, which helps reducing the high costs usually caused
by the amount of manual work required otherwise.
The novel approach presented in this thesis avoids manual report generation and
minimizes any contract with respect to the location of manually created reports, hence
leading to better usability and performance. The approach and its tool support are illustrated
with an ongoing example, validated with a case study, and verified through testing.
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Combining Business Intelligence, Indicators, and the User Requirements Notation for Performance MonitoringJohari Shirazi, Iman 26 November 2012 (has links)
Organizations use Business Intelligence (BI) systems to monitor how well they are meeting
their goals and objectives. Yet, very often BI systems do not include clear models of
the organization’s goals or of how to measure whether they are satisfied or not. Several
researchers now attempt to integrate goal models into BI systems, but there are still major
challenges related to how to get access to the BI data to populate the part of the goal
model (often indicators) used to assess goal satisfaction.
This thesis explores a new approach to integrate BI systems with goal models. In
particular, it explores the integration of IBM Cognos Business Intelligence, a leading BI
tool, with an Eclipse-based goal modeling tool named jUCMNav. jUCMNav is an open
source graphical editor for the User Requirements Notation (URN), which includes the
Use Case Map notation for scenarios and processes and the Goal-oriented Requirement
Language for business objectives. URN was recently extended with the concept of Key
Performance Indicator (KPI) to enable performance assessment and monitoring of business
processes. In jUCMNav, KPIs are currently calculated or modified manually. The
new integration proposed in this thesis maps these KPIs to report elements that are generated
automatically by Cognos based on the model defined in jUCMNav at runtime, with
minimum effort. We are using IBM Cognos Mashup Service, which includes web services
that enable the retrieval of report elements at the most granular level. This transformation
provides managers and analysts with useful goal-oriented and process-oriented
monitoring views fed by just-in-time BI information. This new solution also automates
retrieving data from Cognos servers, which helps reducing the high costs usually caused
by the amount of manual work required otherwise.
The novel approach presented in this thesis avoids manual report generation and
minimizes any contract with respect to the location of manually created reports, hence
leading to better usability and performance. The approach and its tool support are illustrated
with an ongoing example, validated with a case study, and verified through testing.
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Combining Business Intelligence, Indicators, and the User Requirements Notation for Performance MonitoringJohari Shirazi, Iman January 2012 (has links)
Organizations use Business Intelligence (BI) systems to monitor how well they are meeting
their goals and objectives. Yet, very often BI systems do not include clear models of
the organization’s goals or of how to measure whether they are satisfied or not. Several
researchers now attempt to integrate goal models into BI systems, but there are still major
challenges related to how to get access to the BI data to populate the part of the goal
model (often indicators) used to assess goal satisfaction.
This thesis explores a new approach to integrate BI systems with goal models. In
particular, it explores the integration of IBM Cognos Business Intelligence, a leading BI
tool, with an Eclipse-based goal modeling tool named jUCMNav. jUCMNav is an open
source graphical editor for the User Requirements Notation (URN), which includes the
Use Case Map notation for scenarios and processes and the Goal-oriented Requirement
Language for business objectives. URN was recently extended with the concept of Key
Performance Indicator (KPI) to enable performance assessment and monitoring of business
processes. In jUCMNav, KPIs are currently calculated or modified manually. The
new integration proposed in this thesis maps these KPIs to report elements that are generated
automatically by Cognos based on the model defined in jUCMNav at runtime, with
minimum effort. We are using IBM Cognos Mashup Service, which includes web services
that enable the retrieval of report elements at the most granular level. This transformation
provides managers and analysts with useful goal-oriented and process-oriented
monitoring views fed by just-in-time BI information. This new solution also automates
retrieving data from Cognos servers, which helps reducing the high costs usually caused
by the amount of manual work required otherwise.
The novel approach presented in this thesis avoids manual report generation and
minimizes any contract with respect to the location of manually created reports, hence
leading to better usability and performance. The approach and its tool support are illustrated
with an ongoing example, validated with a case study, and verified through testing.
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