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AMCS Seminar: Asymptotic properties of maximum likelihood estimator for the growth rate of jump-type CIR processes

Start Date: December 10, 2018
End Date: December 10, 2018

By Professor Ahmed Kebaier (University Paris 13, France)

We consider a jump-type Cox-Ingersoll-Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to so-called basic affine jump–diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution, where the almost sure limit of an appropriately scaled jump-type supercritical CIR process comes into play. This is a new phenomenon, compared to the critical case, where a diffusion-type critical CIR process plays a role. In the last part of the talk we extend our results to a stable Cox-Ingersoll-Ross process driven by a standard Wiener process and a spectrally positive stable Lévy process.
 
Biography: Associate Professor in Applied Mathematics at University Paris 13. Ahmed Kebaier is member of the laboratory LAGA at UP13 and of the CERMICS research team in Ecole des Ponts Paris Tech. At the engeniering school Sup-Galilée (MACS), Ahmed Kebaieris in charge of the finance track. His main research interests are related to numerical probability and statistics with applications to financial mathematics. He is the instructor of : Monte Carlo methods MAE51 at ENSTEA Paris Tech and Numerical Analysis in the Master Msc international Finance at HEC, Paris (2nd worldwide in Financial Times ranking 2018) and statistics at the Master Financial Engineering, Modeling, Simulation and Data Analytics at Sorbonne Université and Ecole polytechnique.
 

More Information:

For more info contact: Prof. Raul Tempone: email: raul.tempone@kaust.edu.sa
 
Date: Monday 10th Dec 2018
Time:11:00 AM - 12:00 PM
Location: Building 1, level 4, room 4214
Refreshments: Light refreshments around 10:45