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Statistical Inference for LÚvy Processes
Recent years have witnessed great interest in financial modelsbased on LÚvy processes as possible alternatives to the traditional Black-Scholes model of financial markets. An appealing
feature of models based on LÚvy processes is their ability to reproduce important stylised features of financial time series. Moreover, there exists a well-developed mathematical
(probabilistic) theory for LÚvy processes. As any stochastic model, a financial model based on a LÚvy 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. LÚvy processes also find numerous applications in natural sciences, for instance in physics, where closely related concepts of LÚvy walks and LÚvy flights play an important role in modelling the so-called anomalous diffusion phenomena. In fact, some of the popular LÚvy 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 LÚvy 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 LÚvy processes, implementation and theoretical analysis of (non-parametric) Bayesian approach to inference in LÚvy models, handling multivariate LÚvy processes and stochastic differential equations driven by LÚvy processes, statistical investigation of LÚvy 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 LÚvy processes and related branches of stochastic analysis, or contributions dedicated to modelling with LÚvy processes. Hence the workshop is also of interest to researchers active in other fields of applications of LÚvy 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: