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Research Interests:

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


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:


Conference Presentations, Seminar Presentations & Workshops: