This course is designed for graduate students working on their thesis. It gives them the opportunity to enhance their writing abilities and develop their critical Thinking. It attempts to help students achieve greater competency in reading, writing, reflection, and discussion emphasizing the responsibilities of written inquiry and structured reasoning. Students are expected to investigate questions that are at issue for themselves and their audience and for which they don’t already have answers. In other words, this course should help students write about what they have learned through their research rather than simply write an argument supporting one side of an issue or another.

The aim of this course is to provide students with the knowledge of what life and health insurance products are available, how are they designed, what advantages and disadvantages they have, how they can be improved and how comparison can be made. Products covered include traditional insurance as well as investment­linked, long­term care, group insurance and retirement plans.

The main objective of this course is to initiate the student to the concept of random processes used in modeling of random phenomena. It focuses on the discrete Markov process or more commonly Markov chains. In the case of homogenous Markov chains we consider the set of States, the transition matrix, the initial distribution and the distributions at different times, the Chapman­Kolmogorov relationship, classification of States (stability, periodicity and recurrence), absorption in stable classes, stationary distribution, Newton diffusion gas problem, problem of the players ruin, one­dimensional random walk, multidimensional random walk. Study of the Poisson process and queues theory.

The objective of the course is to introduce students to scientific research. Topics to be covered are: interest and research objectives; methodologies used in scientific research; how to define a problem; data collection; documentary research; analysis of the collected knowledge; structure of a Master thesis; writing a report; writing the bibliography; making a scientific poster; and how to approach giving an oral presentation.

This course aims to provide students actuarial methods and techniques of insurance to manage the risks of large portfolios of property and casualty insurance. It addresses thus: the basic principles of the risk management, methods of calculating premiums, risk measures and the determination of the margin of solvency as well as economic capital, the correlation between insured risks and consequences, long­ term balance of the operations of a company and the management of multiple risks.

In this course we study discrete stochastic processes and their applications in finance (pricing of certain types of options, coverage of a portfolio, etc...). It begins with the foliation of various types of process, then we consider the concept of the conditional expectation, filtration, adapted and predictable process, Doobs decomposition of a process, then we develop the theory discrete­ time martingales and stopping times are studied. The remaining of this course is designed for applications in finance, considering the financial options, the prices of options, strategies for managing a portfolio, self-financing strategies, arbitrage strategies, hedging strategies of options, the neutralization of the risk, viable and complete markets, then certain types of financial models, the binomial for several periods model and the Cox­Ross­Rubinstein model are studied. This last model will be show as the discretization of the Black­ Scholes model which is a time continuous model.

The objective of the this course is to give an individual who is beginning a career as a retirement plan professional, a general background in qualified plans as a first step toward meeting the challenges of the profession. The course is divided into two parts. Each part is designed to build upon the groundwork established by the other while not duplicating content or presupposing knowledge or experience level. Part 1 introduces qualified retirement plans, and identifies the special characteristics of defined benefit plans and defined contribution plans. The course addresses installing such plans, distinguishing between the types of plan documents, considering the effect a type of business has on the structure, administration of a plan and an awareness of the parties involved in the operation of the plan. Part 2 covers plan administration, including census collection, benefit allocations and coverage and nondiscrimination testing. This course emphasizes daily valuation recordkeeping but includes discussions of balance­forward plans and conversions. Appropriate investments for daily valuation plans and fiduciary considerations including investment fees and revenue sharing are discussed. The processes involved in daily valuation recordkeeping are covered in detail, including daily functions, mutual fund trading and ethics concerning trading errors. Finally, the course discusses plan mergers and plan terminations including the termination of defined benefit plans.

This course is divided into three parts: loss models, risk and ruin, and credibility theory. In part one; we discuss actuarial models for claim losses. The two components of claim losses namely claim frequency and claim severity, are modeled separately, and are then combined to derive the aggregate­ loss distribution. The techniques of convolution and recursive methods are used to compute the aggregate­loss distributions. Part two is about two important and related topics in modeling insurance business: measuring risk and computing the likelihood of ruin. In we introduce various measures of risk, we discuss specific measures such as Value­at­Risk, conditional tail expectation, and the distortion­function approach. We also analyze the probability of ruin of an insurance business in both discrete­time and continuous­time frameworks. Probabilities of ultimate ruin and ruin before a finite time are discussed. We finally show the interaction of the initial surplus, premium loading, and loss distribution on the probability of ruin. In the last part of this course, we study the Credibility theory as a tool providing the basic analytical framework for pricing insurance products. We introduce the classical approach, the Bühlmann approach, the Bayesian method, as well as the empirical implementation of these techniques. Bühlmanns approach provides a simple solution to the Bayesian method and achieves optimality within the subset of linear predictors.

Topics selected from recent literature on Actuarial and Financial Mathematics are studied in depth. Students will participate in a series of conferences presented by experts.

Advanced topics selected from recent literature on Actuarial and Financial Mathematics are studied in depth. Students will participate in a series of conferences presented by experts.

This course focuses on the statistical analysis of time­to­event or survival data. We introduce the hazard and survival functions; censoring mechanisms, parametric and non­ parametric estimation, and comparison of survival curves. We cover continuous and discrete­time regression models with emphasis on Cox's proportional hazards model and partial likelihood estimation. We discuss competing risk models, unobserved heterogeneity, and multivariate survival models including event history analysis. The course emphasizes basic concepts and techniques as well as applications in epidemiology using the statistical packages SPSS and R.

This course aims to instruct students how to examine a time series, to extract its trend and its seasonal components and to master the principal modelling and forecasting methods. It develops the following concepts: modeling by the method of regression, decomposition of a series. Review of outliers, forecasts. Case of correlated disturbances. Deseasonalization by the moving average method. Maintained or cancelled by a moving average series. Average retaining local, medium polynomials under various constraints, minimizing the variance of the disturbance. Capacity for smoothing a moving average. Treatments of the ends. Forecast using smoothing methods. Exponential smoothing, methods of Brown, of Holt & Winters. Second­order stationary processes. Stationarity, autocovariance and autocorrelation. Partial autocorrelation, Durbin algorithm. Infinite moving average process, spectral density. Autoregressive process AR (p), medium­sized mobile MA (q), mobile medium­Autoregressive process ARMA (p, q). Canonical representation. ARIMA and SARIMA process. Introduction to non­linear models (ARFIMA, ARCH).

Topics selected from recent literature on Actuarial and Financial Mathematics are studied in depth. Students will be responsible to present selected topics of the current scientific literature. They will be graded on relevance, critical analysis and presentation.

Master Thesis Report