Passer au contenu

/ Département de mathématiques et de statistique

Je donne

Rechercher

 

Morales, Manuel

Vcard

Associate Professor

Faculty of Arts and Science - Department of Mathematics and Statistics

André-Aisenstadt Office 4215

514 343-6697

Courriels

Affiliations

  • Membre Centre de recherches mathématiques
  • Membre CRM — Centre de recherches mathématiques
  • Membre Institut de valorisation des données
  • Membre IVADO — Institut de valorisation des données

Research area

Student supervision Expand all Collapse all

Financial time series analysis with competitive neural networks Theses and supervised dissertations / 2017-08
Roussakov, Maxime
Abstract
The main objective of this Master’s thesis is in the modelling of non-stationary time series data. While classical statistical models attempt to correct non- stationary data through differencing and de-trending, I attempt to create localized clusters of stationary time series data through the use of the self-organizing map algorithm. While numerous techniques have been developed that model time series using the self-organizing map, I attempt to build a mathematical framework that justifies its use in the forecasting of financial times series. Additionally, I compare existing forecasting methods using the SOM with those for which a framework has been developed and which have not been applied in a forecasting context. I then compare these methods with the well known ARIMA method of time series forecasting. The second objective of this thesis is to demonstrate the self-organizing map’s ability to cluster data vectors as it was originally developed as a neural network approach to clustering. Specifically I will demonstrate its clustering abilities on limit order book data and present various visualization methods of its output.

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes Theses and supervised dissertations / 2014-12
Omidi Firouzi, Hassan
Abstract
The aim of this thesis is to study fundamental problems in financial and insurance mathematics particularly the problem of measuring risk and its application within financial and insurance frameworks. The main contributions of this thesis can be classified in three main axes: the theory of risk measures, the problem of capital allocation and the theory of fluctuation. In Chapter 2, we design new coherent risk measures and study the associated capital allocation in the context of collective risk theory. We introduce the family of Cumulative Entropic Risk Measures. In Chapter 3, we study the optimal portfolio problem for the Entropic Value at Risk coherent risk measure for particular return models which are based on relevant cases of Jump-Diffusion models. In Chapter 4, we extending the notion of natural risk statistics to the multivariate setting. This non-trivial extension will endow us with multivariate data-based risk measures that are bound to have applications in finance and insurance. In Chapter 5, we introduce the concepts of drawdown and speed of depletion to the ruin theory literature and study them for the class of spectrally negative Lévy risk processes.

Estimation du modèle GARCH à changement de régimes et son utilité pour quantifier le risque de modèle dans les applications financières en actuariat Theses and supervised dissertations / 2013-12
Augustyniak, Maciej
Abstract
The Markov-switching GARCH model is the foundation of this thesis. This model offers rich dynamics to model financial data by allowing for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which has prevented maximum likelihood estimation of this model since its introduction, almost 20 years ago. The first half of this thesis provides a solution to this problem by developing two original estimation approaches allowing us to calculate the maximum likelihood estimator of the Markov-switching GARCH model. The first method is based on both the Monte Carlo expectation-maximization algorithm and importance sampling, while the second consists of a generalization of previously proposed approximations of the model, known as collapsing procedures. This generalization establishes a novel relationship in the econometric literature between particle filtering and collapsing procedures. The discovery of this relationship is important because it provides the missing link needed to justify the validity of the collapsing approach for estimating the Markov-switching GARCH model. The second half of this thesis is motivated by the events of the financial crisis of the late 2000s during which numerous institutional failures occurred because risk exposures were inappropriately measured. Using 78 different econometric models, including many generalizations of the Markov-switching GARCH model, it is shown that model risk plays an important role in the measurement and management of long-term investment risk in the context of variable annuities. Although the finance literature has devoted a lot of research into the development of advanced models for improving pricing and hedging performance, the approaches for measuring dynamic hedging effectiveness have evolved little. This thesis offers a methodological contribution in this area by proposing a statistical framework, based on regression analysis, for measuring the effectiveness of dynamic hedges for long-term investment guarantees.

A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models Theses and supervised dissertations / 2012-11
Groparu-Cojocaru, Ionica
Abstract
In this contribution, we introduce a new class of bivariate distributions of Marshall-Olkin type, called bivariate Erlang distributions. The Laplace transform, product moments and conditional densities are derived. Potential applications of bivariate Erlang distributions in life insurance and finance are considered. Further, our research project is devoted to the study of multivariate risk processes, which may be useful in analyzing ruin problems for insurance companies with a portfolio of dependent classes of business. We apply results from the theory of piecewise deterministic Markov processes in order to derive exponential martingales needed to establish computable upper bounds of the ruin probabilities, as their exact expressions are intractable.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics Theses and supervised dissertations / 2012-07
Ben Salah, Zied
Abstract
This thesis consists mainly of three papers concerned with Markov additive processes, Lévy processes and applications on finance and insurance. The first chapter is an introduction to Markov additive processes (MAP) and a presentation of the ruin problem and basic topics of Mathematical Finance. The second chapter contains the paper "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" written with Manuel Morales and that is published in the European Actuarial Journal. This paper studies the ruin problem for a Markov additive risk process. An expression of the expected discounted penalty function is obtained via identification of the Lévy systems. The third chapter contains the paper "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" that is submitted for publication. This paper presents an extension of the expected discounted penalty function in a setting involving aggregate claims modelled by a subordinator, and Brownian perturbation. This extension involves a sequence of expected discounted functions of successive minima reached by a jump of the risk process after ruin. It has important applications in risk management and in particular, it is used to compute the expected discounted value of capital injection. Finally, the fourth chapter contains the paper "The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential" written with Romuald Hérvé Momeya and that is published in the journal Asia Pacific Financial Market. It presents new results related to the incompleteness problem in a financial market, where the risky asset is driven by Markov additive exponential model. These results characterize the martingale measure satisfying the entropy criterion. This measure is used to compute the price of the option and the portfolio of hedging in an exponential Markov-modulated Lévy model.

Les processus additifs markoviens et leurs applications en finance mathématique Theses and supervised dissertations / 2012-05
Momeya Ouabo, Romuald Hervé
Abstract
This thesis focuses on the pricing and hedging problems of financial derivatives in a Markov-modulated exponential-Lévy model. Such model is built on a Markov additive process as much as the Black-Scholes model is based on Brownian motion. Since there exist many sources of randomness, we are dealing with an incomplete market and this makes inoperative techniques initiated by Black, Scholes and Merton in the context of a complete market. We show that, by using some results of the theory of Markov additive processes it is possible to provide solutions to the previous problems. In particular, we characterize the martingale measure which minimizes the relative entropy with respect to the physical probability measure. Also under some conditions, we derive explicitly the optimal portfolio which allows an agent to minimize the local quadratic risk associated. Furthermore, in a more practical perspective we characterize the price of a European type option as the unique viscosity solution of a system of nonlinear integro-di erential equations. This is a rst step towards the construction of e ective numerical schemes to approximate options price.

Densités de copules archimédiennes hiérarchiques Theses and supervised dissertations / 2012-04
Pham, David
Abstract
Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference such as estimation or goodness-of-fit testing it is important to have the density. The present work fills this gap. After a short introduction on copula and nested Archimedean copulas, a general formula for the derivatives of the nodes and inner generators appearing in nested Archimedean copulas is developed. This leads to a tractable formula for the density of nested Archimedean copulas. Various examples including famous Archimedean families and transformations of such are given. Furthermore, a numerically efficient way to evaluate the log-density is presented.

Prédiction de l'attrition en date de renouvellement en assurance automobile avec processus gaussiens Theses and supervised dissertations / 2011-08
Pannetier Lebeuf, Sylvain
Abstract
The field of auto insurance is working by cycles with phases of profitability and other of non-profitability. In the phases of non-profitability, insurance companies generally have the reflex to increase the cost of premiums in an attempt to reduce losses. For cons, very large increases may have the effect of massive attrition of the customers. A too high attrition rate could have a negative effect on long-term profitability of the company. Proper management of rate increases thus appears crucial to an insurance company. This thesis aims to build a simulation tool to predict the content of the insurance portfolio held by an insurer based on the rate change proposed to each insured. A proce- dure using univariate Gaussian Processes regression is developed. This procedure offers a superior performance than the logistic regression model typically used to perform such tasks.

On some aspects of coherent risk measures and their applications Theses and supervised dissertations / 2011-07
Assa, Hirbod
Abstract
The aim of this thesis is to study several aspects of risk measures particularly in the context of financial applications. The primary framework that we use is that of coherent risk measures as defined in Artzner et al (1999). But this is not the only class of risk measures that we study here. We also investigate the concepts of natural risk statistics Kou et al (2006) and convex risk measure Follmer/ and Schied (2002). The main contributions of this Thesis can be classified in three main axes: Capital allocation, risk measurement and capital requirement and solvency. In chapter 2, we characterize risk measures with the Lebesgue property on bounded càdlàg processes. This allows to present two applications in risk assessment and capital allocation. In chapter 3, we extend the concept of natural risk statistics to the space of infinite sequences. This has been done in order to introduce a consistent way of constructing risk measures for data bases of any size. In chapter 4, we discuss the concept of Good Deals and how to deal with a situation where these pathological positions are present in the market. Finally, in chapter 5, we try to relate all three chapters by extending the definition of Good Deals to a larger set of risk measures that somehow includes the discussions in chapters 2 and 3.

Les produits dérivés des marchés européens du carbone Theses and supervised dissertations / 2010-08
Godin, Frédéric
Abstract
During the last decade, the European Union has regulated emissions of Greenhouse Gases on its own territory. Consequently, a European Carbon Market (EU ETS) is currently emerging where CO2 emission certificates (EUA and CER) and derivatives are traded on Exchanges. The objectif of this research is to evaluate and compare different models to represent the emission certificates' price and to price derivatives of the carbon markets.

Étude empirique de distributions associées à la Fonction de Pénalité Escomptée Theses and supervised dissertations / 2010-03
Ibrahim, Rabï
Abstract
We discuss a simulation approach for the joint density function of the surplus prior to ruin and deficit at ruin for risk models driven by Lévy subordinators. This approach is inspired by the Ladder Height decomposition for the probability of ruin of such models. The Classical Risk Model driven by a Compound Poisson process is a particular case of this more generalized one. The Expected Discounted Penalty Function, also referred to as the Gerber-Shiu Function (GS Function), was introduced as a unifying approach to deal with different quantities related to the event of ruin. The probability of ruin and the joint density function of surplus prior to ruin and deficit at ruin are particular cases of this function. Expressions for those two quantities have been derived from the GS Function, but those are not easily evaluated nor handled as they are infinite series of convolutions with no analytical closed form. However they share a similar structure, thus allowing to use the Ladder Height decomposition of the Probability of Ruin as a guiding method to generate simulated values for this joint density function. We present an introduction to risk models driven by subordinators, and describe those models for which it is possible to process the simulation. To motivate this work, we also present an application for this distribution, in order to calculate different risk measures for those risk models. An brief introduction to the vast field of Risk Measures is conducted where we present selected measures calculated in this empirical study. This work contributes to better understanding the behavior of subordinators driven risk models, as it offers a numerical point of view, which is absent in the literature.

Convergence faible de processus de Lévy vers un processus hyperbolique généralisé pour l'évaluation d'options Theses and supervised dissertations / 2007
Joly, Louis-Philippe
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Research projects Expand all Collapse all

Centre de recherches mathématiques (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2022 - 2029

Fraud Detection in Derivatives Market using Graph Neural Network (GNN) MITACS Inc. / 2022 - 2023

Leveraging artificial intelligence to improve Environmental, Social, and Governance (ESG) data and assess the quality of ESG reports CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2022 - 2023

Machine Learning and AI for the Global Futures Markets MITACS Inc. / 2022 - 2022

Usages et valeur des données non traditionnelles en science actuarielle Fondation de l'UQAM / 2022 - 2022

Réseaux Mathematics for public health (MfPH)_Project 3_Risk Evaluation and Early Detection of Emerging Infectious Disease Outbreaks in Canada CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2021 - 2023

Anomaly detection to identify insider threats in the banks and companies MITACS Inc. / 2021 - 2022

Development of Machine Learning Methods to Improve ESG Scores and Responsible Investment Decisions MITACS Inc. / 2021 - 2022

Fraud Detection in Derivatives Market using Deep Unsupervised Anomaly Detection and NLP MITACS Inc. / 2021 - 2022

Anomaly detection to identify insider threats in the banks and companies MITACS Inc. / 2021 - 2021

Anonymisation et désensibilisation de données MITACS Inc. / 2021 - 2021

Futures First Algorithmic Derivatives Trading MITACS Inc. / 2021 - 2021

Statistical Arbitrage of Internationally Interlisted Stocks SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2020 - 2024

Deep Unsupervised Anomaly Detection in Options Markets MITACS Inc. / 2020 - 2021

Supplément COVID-19 CRSNG_Beyond the Ruin Problem: Novel applications of Insurance Risk Models CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2020 - 2021

Apogée Canada fonds d'excellence en recherche // Programme de démarrage de projets de recherche collaborative Holt Accelerator SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2020 - 2020

Axionable_Prog de démarrage de projets de rech collaborative avec les membres insustriels d'IVADO_PROJET DE DÉTECTION DE TRANSACTIONS ANORMALES DANS LE MARCHÉ DES OPTIONS Axionable Canada inc. / 2020 - 2020

Programme de démarrage de projet de recherche collaborative d'Axionable SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2020 - 2020

Conception d’analytique avancée à la Banque Nationale (BNC) / Stagiaire(s) : Megan Cao, Amirreza Mafi, Marzieh Mehdizadeh, Mohamed Abdelsalam, Farnaz Arezi MITACS Inc. / 2019 - 2019

NSERC CREATE Program on Machine Learning in Quantitative Finance and Business Analytics CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2018 - 2025

Beyond the Ruin Problem: Novel applications of Insurance Risk Models CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2018 - 2024

Apogée Canada fonds d'excellence en recherche / Compte pour le paiement des salaires de Gabriel Yergeau SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2018 - 2020

Investment Portfolio Design and Optimal Execution of Automated Trading Strategies : An Exploratory Research Program. MITACS Inc. / 2018 - 2019

Machine Learning Strategies in the Physical North American Power Markets / Stagiaire(s) : Marie-Ève Malette MITACS Inc. / 2018 - 2019

Modeling regime changes to improve portfolio diversification and performance MITACS Inc. / 2018 - 2019

Credit Card Fraud Detection Using Machine Learning Banque nationale du Canada / 2018 - 2018

Application des méthodes d'apprentissage machine au problème d'inventaire dans les stratégies algorithmiques à haute fréquence: Une approche via un simulateur du marché / 2017 - 2019

Application des méthodes d'apprentissage machine au problème d'inventaire dans les stratégies algorithmiques à haute fréquence: Une approche via un simulateur du marché. / 2017 - 2019

Credit Card Fraud Detection Using Machine Learning. PROMPT / 2017 - 2019

Méthodes de prévision non-parametriques dans la modélisation des prix d'électricité et leurs applications au design des portefeuilles optimaux des contrats "day-ahead" / 2017 - 2018

Méthodes de prévision non-paramétriques dans la modélisation des prix d’électricité et leurs applications au dseign des portefeuilles optimaux des contracts day-ahead» PROMPT / 2017 - 2018

Automated Transaction Classification Using Machine Learning Algorithm. MITACS Inc. / 2017 - 2017

Exploring Optimal Trading Rules in a High-Frequency Portfolio MITACS Inc. / 2017 - 2017

Implementing Factor Models in Investment Management. / 2017 - 2017

Conception et implémentation d'un modèle d'évaluation pour les prix des contrats à terme dans les marchés d'électricité CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2016

CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2023

Évaluation de la performance et l'impact de marché d'une stratégie "market making" à haute fréquence avec un simulateur de bourse. CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2015 - 2017

Conception d'un modèle de simulateur de bourse et son application dans le ''trading'' algorithmique: le défi de la réplication de la microstructure des marchés à haute fréquence CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2015 - 2016

Développement d'approches statistiques pour l'analyse de portefeuilles d'investissements alternatifs. MITACS Inc. / 2015 - 2015

(BOURSE OLIVIER LECOMPTE) ETUDE COMPARATIVE DE LA PERFORMANCE DES MODELES NON-GAUSSIEN DANS L'EVALUATION DES PRODUITS DERIVES Innovation, Sciences et Développement économique Canada / 2014 - 2014

DESIGN AND IMPLEMENTATION OF A VIABLE REGIME-SWITCHING MODEL FOR ASSET PRICES WITH A VIEW TOWARDS PORTFOLIO MANAGEMENT CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2014 - 2014

DESIGNING TAILOR-MADE RISK MEASURES FOR INSURANCE AND FINANCIAL APPLICATIONS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2013 - 2019

CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016

SOME ASPECTS OF THE INTERPLAY BETWEEN INSURANCE AND FINANCIAL RISKS / 2008 - 2012

Selected publications Expand all Collapse all

Computing the finite-time expected discounted penalty function for a family of Lévy risk processes

Kuznetsov, Alexey et Morales, Manuel, Computing the finite-time expected discounted penalty function for a family of Lévy risk processes , 1--31 (2014), , Scand. Actuar. J.

Lévy systems and the time value of ruin for Markov additive processes

Ben Salah, Zied et Morales, Manuel, Lévy systems and the time value of ruin for Markov additive processes 2, 289--317 (2012), , Eur. Actuar. J.

Risk measures on the space of infinite sequences

Assa, Hirbod et Morales, Manuel, Risk measures on the space of infinite sequences 2, 253--275 (2010), , Math. Financ. Econ.

On a generalization of the Gerber-Shiu function to path-dependent penalties

Biffis, Enrico et Morales, Manuel, On a generalization of the Gerber-Shiu function to path-dependent penalties 46, 92--97 (2010), , Insurance Math. Econom.

Fourier inversion formulas in option pricing and insurance

Dufresne, Daniel, Garrido, Jose et Morales, Manuel, Fourier inversion formulas in option pricing and insurance 11, 359--383 (2009), , Methodol. Comput. Appl. Probab.

Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density

Bahsoun, Wael, Góra, Pawel, Mayoral, Silvia et Morales, Manuel, Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density 23, 181--212 (2007), , Appl. Stoch. Models Bus. Ind.

On the expected discounted penalty function for a perturbed risk process driven by a subordinator

Morales, Manuel, On the expected discounted penalty function for a perturbed risk process driven by a subordinator 40, 293--301 (2007), , Insurance Math. Econom.

On the expected discounted penalty function for Lévy risk processes

Garrido, José et Morales, Manuel, On the expected discounted penalty function for Lévy risk processes 10, 196--218 (2006), , N. Am. Actuar. J.

Risk theory with the generalized inverse Gaussian Lévy process

Morales, Manuel, Risk theory with the generalized inverse Gaussian Lévy process 34, 361--377 (2004), , Astin Bull.

On a surplus process under a periodic environment: a simulation approach

Morales, Manuel, On a surplus process under a periodic environment: a simulation approach 8, 76--89 (2004), , N. Am. Actuar. J.

On an approximation for the surplus process using extreme value theory: applications in ruin theory and reinsurance pricing

Morales, Manuel, On an approximation for the surplus process using extreme value theory: applications in ruin theory and reinsurance pricing 8, 46--66 (2004), , N. Am. Actuar. J.

A risk model driven by Lévy processes

Morales, Manuel et Schoutens, Wim, A risk model driven by Lévy processes 19, 147--167 (2003), , Appl. Stoch. Models Bus. Ind.