Probability and Statistics Research Seminars
2nd Semester 2009/2010
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17 Februaryt.b.a.
2010
Juhyun Park (Lancaster University)
2.15pm - G.114, Alan Turing BuildingAbstractAbstract will appear here
3 Marcht.b.a.
2010
Tatjana Chudjakow (University Bielefeld)
2.15pm - G.114, Alan Turing BuildingAbstract3 MarchOn solving optimal stopping problems for Lévy processes in finite horizon
2010
Elena Boguslavskaya (London School of Economics)
3.15pm - G.114, Alan Turing BuildingAbstractWe present a way to solve optimal stopping problems with finite (or infinite) horizon for a Lévy process. We pay special attention to the case when the gain function is analytic and monotone. The main tool in our method is to construct the appropriate Appell function, and, consequently, find the optimal stopping boundary. Finally, we illustrate our method by several examples.
10 Marcht.b.a.
2010
Ashkan Nikeghbali (University Zürich)
2.15pm - G.114, Alan Turing BuildingAbstract10 Marcht.b.a.
2010
Leonid V. Bogachev (University of Leeds)
3.15pm - G.114, Alan Turing BuildingAbstract17 MarchVon Neumann-Gale Dynamical Systems and their Applications in Finance
2010
Igor Evstigneev (University of Manchester)
2.15pm - G.114, Alan Turing BuildingAbstractVon Neumann-Gale dynamical systems are defined in terms of multivalued operators possessing certain properties of convexity and homogeneity. These operators assign to each element of a given cone a convex subset of the cone describing possible one-step transitions from one state of the system to another. The classical, deterministic theory of such dynamics was originally aimed at the modelling of economic growth (von Neumann 1937 and Gale 1956). First attempts to build a stochastic generalization of this theory were undertaken in the 1970s by Dynkin, Radner and their research groups. However, the initial attack on the problem left many questions unanswered. Substantial progress was made only in the late 1990s, and final solutions to the main open problems were obtained only in the last two or three years. Recently it has been observed that stochastic analogues of von Neumann-Gale systems provide a natural and convenient framework for financial modelling (asset pricing and hedging under transaction costs, capital growth theory). This observation gave a new momentum to studies in the field and posed new interesting questions. The talk will give an introduction into the theory, review recent progress and discuss applications.
24 MarchBand-limited Stochastic Processes In Discrete And Continuous Time
2010
D.S.G. Pollock (University of Leicester)
2.15pm - G.114, Alan Turing BuildingAbstractBAND-LIMITED STOCHASTIC PROCESSES IN DISCRETE AND CONTINUOUS TIME
By D.S.G. POLLOCK
University of Leicester
Email: stephen_pollock@sigmapi.u-net.com
In the theory of stochastic differential equations, it is commonly assumed that the forcing function is a Wiener process. Such a process has an infinite bandwidth in the frequency domain. In practice, however, all stochastic processes have a limited bandwidth. A theory of band-limited linear stochastic processes is described that reflects this reality, and it is shown how the corresponding ARMA models can be estimated. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by resampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process.21 Aprilt.b.a.
2010
Niels Jacob (Swansea University)
2.15pm - G.114, Alan Turing BuildingAbstract21 Aprilt.b.a.
2010
Dan Crisan (Imperial College London)
3.15pm - G.114, Alan Turing BuildingAbstract28 Aprilt.b.a.
2010
Prakash Patil (University )
2.15pm - G.114, Alan Turing BuildingAbstractAbstract will appear here
5 Mayt.b.a.
2010
J N S Matthews (Newcastle University)
2.15pm - G.114, Alan Turing BuildingAbstractAbstract will appear here
12 Mayt.b.a.
2010
Annie Millet (Université Paris 1)
2.15pm - G.114, Alan Turing BuildingAbstract12 Mayt.b.a.
2010
Ming-Yen Cheng (UCL)
4pm - t.b.a., Alan Turing BuildingAbstractAbstract will appear here
6 JanuaryVariable Selection for Censored Linear Regression Models: A New Perspective. (seminar cancelled due to bad weather)
2010
Yi Li (Harvard University, USA)
2.15pm - G.207, Alan Turing BuildingBack to Probability and Statistics Research SeminarsAbstractThe Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. A key advantage is that it does not pertain to a particular likelihood or objective function, as opposed to the existing penalized likelihood methods, and hence has the potential for wide applications. To our knowledge, most work has been performed with fully observed response variables. This talk discusses a new class of adaptive Dantzig variable selectors for linear regression models when the response variable is subject to right censoring. This is motivated by a clinical study of detecting predictive genes for myeloma patients' event-free survival, which is subject to right censoring. Under some mild conditions, we establish the theoretical properties of our procedures, including consistency in model selection (i.e. the right subset model will be identified with a probability tending to 1) and the oracle property of the estimation (i.e. the asymptotic distribution of the estimates is the same as that when the true subset model is known a priori). The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply the new method to the aforementioned myeloma clinical trial and identify important predictive genes for patients' event free survival.
Further information
For further information contactDr Georgi Boshnakov (statistics) or
Dr Markus Riedle (probability)