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The Department of Statistics & Operation Research, within the  Faculty of Science, is organising a seminar as part of their series of departmental seminars for this academic year, entitled 'Estimation of Transformed Lévy Measures'.

The seminar will be held on Friday 22 February at 12:00 in Lab Room 602 of the Maths & Physics Building.

Speaker 
Dr Mark Anthony Caruana

Abstract
The estimation of Lévy processes has become a very popular topic in the past decades. This is because that such processes have been used extensively in various fields of research, most prominently in finance.

We will discuss various nonparametric techniques which can be used to estimate a transformed version of the Lévy measure. Rates of convergence are also discussed. Then we move a step forward by finding the optimal approximation of the measure associated to a transformed version of Lévy-Khintchine canonical representation via a convex combination of a finite number P of Dirac masses. The quality of such an approximation is measured in terms of the Monge-Kantorovich or the Wasserstein metric. In essence, this procedure is equivalent to the quantisation of measures. This procedure requires prior knowledge of the functional form of the measure. However, since this is in general not known, we shall have to estimate it. It will be shown that the objective function used to estimate the position of the Dirac masses and their associated weights can be expressed as a stochastic program. The properties of the estimator provided are discussed. Also, a number of simulations for different types of Lévy processes are performed and the results are discussed.