Statistical Inference for Lévy Processes

Recent years have witnessed great interest in financial modelsbased on Lévy processes as possible alternatives to the traditional Black-Scholes model of financial markets. An appealing

feature of models based on Lévy processes is their ability to reproduce important stylised features of financial time series. Moreover, there exists a well-developed mathematical

(probabilistic) theory for Lévy processes. As any stochastic model, a financial model based on a Lévy process depends on various parameters (finite, or possibly infinite-dimensional).

Estimation of these parameters (or calibration of the model to the financial data) is of critical

importance to successful application of such a model in practice. This is a new and challenging area of statistical research. Lévy processes also find numerous applications in natural sciences, for instance in physics, where closely related concepts of Lévy walks and Lévy flights play an important role in modelling the so-called anomalous diffusion phenomena. In fact, some of the popular Lévy models used in finance, such as the normal inverse Gaussian model, have been proposed earlier in other contexts in the natural sciences. Furthermore, (the laws of) the processes with independent increments are rather useful in non-parametric Bayesian statistics, where they are used as priors, for instance in survival analysis models.

The workshop aims to contribute to the development of this area and will bring together leading researchers in the field. They will overview recent progress achieved in inference methods for Lévy processes, identify problems of interest and outline future research directions. Topics like inverse statistical problems, regularisation techniques, semi- and nonparametric statistics, adaptive inference, are expected to play a major role. Among many open problems and challenges facing the area we mention e.g. devising computationally efficient inference strategies for Lévy processes, implementation and theoretical analysis of (non-parametric) Bayesian approach to inference in Lévy models, handling multivariate Lévy processes and stochastic differential equations driven by Lévy processes, statistical investigation of Lévy copulas, incorporation of techniques and themes current in other branches of statistics (e.g. sparsity), and others. However, the workshop themes will not be limited to statistics only, but will also feature a number of contributions dealing with probabilistic aspects of Lévy processes and related branches of stochastic analysis, or contributions dedicated to modelling with Lévy processes. Hence the workshop is also of interest to researchers active in other fields of applications of Lévy processes.

Lorentz Center does not charge registration fees. In addition, Lorentz Center hosts a welcome reception and a workshop dinner, both free of charge.

This workshop is financially supported by:

·         Universiteit van Amsterdam

·         Elsevier

·         STAR

·         NWO

·         Mathematisch Instituut Leiden

·         Stichting Compositio