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Time series analysis, Stochastic Models of Financial and Actuarial Mathematics, Lévy Driven CARMA Models, Parametric and Nonparametric Goodness of Fit Tests.

** Introduction: **

In keeping with the Nobel prize winning work of Black, Scholes (1973) and Merton (1973) that proposed a continuous-time stochastic model for option pricing, researchers have long recognized that continuous-time models are needed to represent the reality of the economy and financial markets.
A continuous time model reflects the natural evolution of a process indexed by an interval I ⊆ R and the choice of an appropriate stochastic model is essential. Thus, it is critical to test how well the proposed model represents the observed behavior of the process - in other words, we must assess the "goodness-of-fit" of our model. However, in reality most frequently the continuous time process can only be observed at discrete times. Reconciling the discrete data with the continuous model is the principal motivation for my work. The recent availability of high-frequency (or tick-by-tick transaction) data of various financial markets allows us to closely approximate the behavior of the continuous time process.

My research focuses on checking and fitting models for high and moderate frequency data used in various areas of application but mainly in finance due to the availability of the financial securities data. I consider stochastic models of financial and actuarial mathematics such as Lévy-driven continuous ARMA processes; I try go beyond exploratory data analysis and try to provide formal tests to fit data observed at discrete times. The topics range from deep theoretical work to direct applications for either real or simulated data. If you are interested in working with me please do not hesitate to contact me.

** Projects (Papers) in Preparation: **

- Model checking: Realized Volatility Model Lévy-driven CARMA(2,1).

- I. Abdelrazeq, B.G. Ivanoff, and R. Kulik, Goodness of fit test: Recovered noise of CAR(1) processes.

- I. Abdelrazeq, Model verification for Lévy-driven Ornstein-Uhlenbeck processes with estimated parameters. Statistics and Probability Letters, V: 104, P. 26-35, 2015.

- I. Abdelrazeq, B.G. Ivanoff, and R. Kulik, Model Verification for Lévy-driven Ornstein-Uhlenbeck Processes. Electronic Journal of Statistics, 8(1):1029– 1062, 2014.

- Lévy-Driven CARMA(2,1): Checking the Model Assumption. 44th Annual Meeting of the Statistical Society of Canada May 29-June 1, 2016 at Brock University St. Catharines, Ontario.

- Model Checking and Fitting: Lévy-Driven CARMA. Workshop in Stochastic Process in honor of Professor Gail Ivanoff, May 29, 2015, at University of Ottawa.

- Goodness of Fit Test: Recovered Noise for CAR(1) Processes. 42nd Annual Meeting of the Statistical Society of Canada May 25-28, 2014 at the University of Toronto, Toronto, Ontario.

- Model Checking: Lévy-driven Ornstein-Uhlenbeck Processes. Joint Mathematical Meeting, January 15, 2014, Baltimore, Maryland.

- General Study: Model Verification for Lévy-driven Ornstein-Uhlenbeck Processes. Seminar Presentation, December 13, 2013 at University of Ottawa, Ottawa, Ontario.

- Model Checking: Lévy-driven CAR(1) Processes. Statistical Society of Ottawa, 4th Annual Student Research Day, September 27, 2013 at University of Ottawa, Ottawa, Ontario.

- Inference for Discretely Observed Lévy-driven Ornstein-Uhlenbeck Processes. 41st Annual Meeting of the Statistical Society of Canada, May 26-29, 2013 at the University of Alberta, Edmonton, Alberta.

- Estimation and Modeling Problems in Financial Engineering Workshop, Bruno Rmillard, HEC Montral. 41st Annual Meeting of the Statistical Society of Canada, May 26-29, 2013 at the University of Alberta, Edmonton, Alberta.

- MAA Minicourse: Introductory statistics using randomization and bootstrap methods, JMM, Baltimore, Maryland.