Actuarial and Financial Mathematics

Source: Luis Villa del Campo, Times Square - NASDAQ

Program Description

Actuarial and financial mathematics are mathematics applied to insurance and finance problems. The group concentrates its activites on the development and use of probabilistic and statistical methods to analyze problems with a financial impact on society. The promotion of graduate studies in actuarial and financial mathematics is also at the heart of the mission of the group.

The research interests, and therefore also teaching interests, of the members are generally in the area of property and casualty insurance and actuarial statistics, actuarial finance and financial mathematics, as well as the mathematics of risk and ruin theory. In particular:

  • ratemaking and loss reserving for property and casualty insurance
  • solvency of financial institutions
  • financial and actuarial innovation in insurance: pricing and hedging for variable annuities and equity-linked insurance products
  • impact of natural catastrophes, climate change and other extreme risks
  • dependence models
  • risk measures
  • claims frequency and severity models
  • stochastic control of risk processes and stochastic optimization
  • Big Data in insurance

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Program Members

2020-21 Course Listings

Fall

Credibility Theory

The course looks at statistical estimation techniques for insurance data with heterogeneous risk classes.  Two classical approaches to credibility theory are discussed: limited fluctuations and greatest accuracy.  Topics covered include American, Bayesian and exact credibility.  Bühlmann, Bühlmann-Straub, hierarchical and regression credibility models are derived.  Generalized linear models, credibility regression trees and the issue of robustness will also be discussed. The course prepares for the Credibility part of the Society of Actuaries Exam STAM and the Casualty Actuarial Society Exam MAS II and give partial exemption from the Canadian Institute of Actuaries.

Prof. Ioana Groparu

MAST 725 (MAST 881D)

Institution: Concordia University

Mathematical and Computational Finance II

This course focuses on computational aspects, implementation, continuous-time models, and advanced topics in Mathematical and Computational Finance.  We shall cover the following topics (time permitting):

  • Calibration and implementation
  • Brownian motion and stochastic calculus
  • Elements of continuous time finance
  • PDE methods
  • Monte-Carlo methods
  • Exotic derivatives
  • Risk management
  • Other topics

Prof. Cody Hyndman

MAST 729A (MAST 881A)

Institution: Concordia University

Analyse mathématique du risque

Mesures et comparaison des risques, Théorie de la ruine en temps discret et continu, Mouvement brownien et temps de premier passage, Modèles de risque de crédit, Concepts et mesures de dépendance, Copules, Applications des modèles de dépendance en actuariat et en finance.

Prof. Mathieu Boudreault

MAT 8600

Institution: Université du Québec à Montréal

Méthodes stochastiques en finance I

Modèles discrets. Stratégies de transaction. Arbitrage. Marchés complets. Évaluation des options. Problème d'arrêt optimal et options américaines. Mouvement brownien. Intégrale stochastique, propriétés. Formule d'Itô. Localisation. Introduction aux équations différentielles sotchastiques. Changement de probabilité et théorème de Girsanov. Représentation des martingales et stratégie de couverture. Modèle de Black et Scholes.

 

Prof. Clarence Simard

MAT 8601

Institution: Université du Québec à Montréal

Mesure et probabilités

Tribus et variables aléatoires. Théorie de l'intégration: théorème de Lebesgue, espace Lp, théorème de Fubini. Construction de mesures, mesure de Radon. Indépendance. Conditionnement.

 

Prof. Anne Mackay et Jean-François Renaud

MAT 7070

Institution: Université du Québec à Montréal

Winter

Finance mathématique

Structures à terme, processus stochastiques, modèles et produits dérivés de taux d'intérêt, immunisation et appariement, produits dérivés de crédit, titres adossés à des créances hypothécaires, volatilité.

Prof. Manuel Morales

ACT 6230

Institution: Université de Montréal

Risk analytics in Insurance and Credit Risk with R

This course is an introduction to the analysis of individual risks encountered in various insurance and credit risk contexts, such as risk scoring and pricing, capital reserving, marketing and claims management. In the past, modeling techniques for insurance and credit risks have been developed separately, and the aim is to put together an inventory of relevant results on such individual risks that are currently scattered in these two domains. Special emphasis will be placed on their implementation using R. 

Prof. Yang Lu

MAST 729/881/4

Institution: Concordia University

Laboratoire de modélisation de données financières

Prof. Manuel Morales

ACT 6240

Institution: Université de Montréal

Contrôle stochastique optimal et applications

Ce cours-séminaire est une introduction au contrôle stochastique optimal. Il portera principalement sur la résolution du problème de dividendes optimales de Bruno de Finetti et les variantes publiées plus récemment.

Pré-requis: connaissances élémentaires sur le mouvement brownien, la formule d'Itô et le processus de Poisson composé.

 If needed, this course will be given in English.

Prof. Jean-François Renaud

MAT 998L

Institution: Université du Québec à Montréal