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Event(s) on January 2013
- Thursday, 3rd January, 2013
Title: Robust Utility Maximisation Via Second Order BSDEs Speaker: Dr. ZHOU Chao , Department of Mathematics, National University of Singapore, Singapore Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The problem of robust utility maximisation in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this problem in the framework of second order backward stochastic differential equations (2BSDEs for short) with quadratic growth generators. We show for exponential, power and logarithmic utilities that the value function of the problem can be written as the initial value of a particular 2BSDE and prove existence of an optimal strategy. Finally several examples which shed more light on the problem and its links with the classical utility maximization one are provided. In particular, we show that in some cases, the upper bound of the volatility interval plays a central role, exactly as in the option pricing problem with uncertain volatility models. - Friday, 4th January, 2013
Title: DLS: Subspace Technique for Nonlinear Optimization Speaker: Prof. Ya-xiang Yuan, Chinese Academy of Sciences, China Time/Place: 16:30 - 17:30 (Preceded by Reception at 16:00)
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we review various subspace techniques that are used in constructing of numerical methods for nonlinear optimization. The subspace techniques are getting more and more important as the optimization problems we have to solve are getting larger and larger in scale. Subspace techniques have the advantage of reducing both computation cost and memory size. The essential part of a subspace method is how to choose the subspace in which the trial step or the trust region should belong. Examples of applications of subspace techniques are also presented. - Monday, 14th January, 2013
Title: CMIV Seminar: Robust Statistical Ranking on Graphs Speaker: Prof. Yuan YAO, School of Mathematical Sciences, Peking University Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The problem of ranking or rating based on pairwise comparisons, as an uni-dimensional scaling, is a fundamental problem which can be traced back at least to the $18^{th}$ century. Recently we are witnessing a rapid growth of paired comparison data which are imbalanced, incomplete, and distributed on a graph, for example the crowdsourcing experiments on Internet. Quality of such data collection is an important problem where the existence of outliers may cause instability to the inference of global ranking. To reach a robust global ranking with paired comparison data on graphs, in this paper we present a systematic analysis on a general linear model in the presence of sparse outliers and Gaussian-type noise. Exterior calculus on graphs plays a central role to form an unified framework. We present various conditions under which outliers can be detected and the underlying global ranking function can be recovered, exactly or approximately. - Wednesday, 16th January, 2013
Title: Mathematical modeling of renal hemodynamics: Feedback dynamics and coupled oscillators Speaker: Dr. Anita T. Layton, Department of Mathematics, Duke University, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We have formulated a mathematical model for the rat afferent arteriole (AA), glomerulus, and short loop of Henle, and used that model to study the interactions between the tubuloglomerular feedback (TGF) and myogenic mechanism, the two key mechanisms that mediate renal autoregulation. Blood flow is described by Poiseuille flow. The AA model consists of a series of arteriolar smooth muscle cells, each of which represents ion transport, cell membrane potential, cellular contraction, gap junction coupling, and wall mechanics. The myogenic response representation is based on the hypothesis that the voltage dependence of calcium channel openings responds to transmural pressure so that the vessel constricts when pressure increases. The glomerular filtration model is based on the model by Deen et al. (AJP 1972). The TGF model represents the pars recta, descending limb, and thick ascending limb, and predicts tubular fluid flow rate and [Cl-] along the loop. The model can be used as a fundamental component in a multi-scale renal microvasculature model for investigations of pathogenesis of hypertensive renal diseases. This research was supported in part by NIH grant DK-89066 and NSF grant DMS-0715021. - Wednesday, 16th January, 2013
Title: Testing the distribution specification in multiparameter local likelihood models Speaker: Prof. CHENG Ming-Yen, Department of Mathematics , National Taiwan University , Taiwan Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Multiparameter local likelihood models have been accepted as a flexible tool for modeling the relationship between responses and covariates, and the corresponding methodology has been used to analyze data arising from climatology, environmetrics, finance, medicine, and so on. Although both point and interval estimation for the unknown parameter functions in the model have been investigated in the literature, how to formally test goodness-of-fit of the specified form of the conditional density function remains an unsolved problem. Testing the specification of the conditional density is an important issue, the inference becomes inclusive or misleading and the estimated parameter functions become meaningless if the form of the true conditional density is different from the specified one. In this paper, we address this specification test problem. Our tests are developed using ideas of probability integral transformation and the well-known Kolmogorov-Smirnov and Cramer-von Mises test statistics. We show that formal tests can be constructed if undersmoothing is employed. The asymptotic null distributions of the proposed test statistics depend on the unknown parameter functions, so parametric bootstrap tests are suggested. We conducted a simulation study to assess finite sample properties of the proposed test and applied it to validate the generalized extreme value local likelihood model for an environmental data set. - Wednesday, 16th January, 2013
Title: Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors Speaker: Prof. WU Hau-Tieng, The Program in Applied and Computational Mathematics, Princeton University, USA Time/Place: 15:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Seasonality (or periodicity) and trend are features describing an observed time se-ries, for example, the incidence time series of certain event. Extracting these features from the time series is an important issue in many scienti_c _elds, like public health, medicine, economics, astronomy et al. Many methods are available for this purpose. However, it is not an easy task to analyze the dynamical behavior of seasonality, such as time-varying periods and amplitude modulations, and trend by existing method-s, and the adaptivity of the analysis to such dynamics is not guaranteed. Another challenge is to ensure robustness of the methodology to dependent and heteroscedas-tic errors. These tasks are even more complicated when there are multiple periodic components. We consider the problem of the following form: given a function f(t) = sum^K_(k=1) A_k(t) cos(phi_k(t)), A_k(t), phi'_k(t)>0 for all t, compute Ak(t) and ϕ′k(t) or describe their properties from f. This general model is aimed to describe the dynamics of possibly multi-component seasonality (or pe-riodicity) and trend. With this model, we introduce an adaptive method, referred to as the Synchrosqueezing transform, to accurately extract information on these features from a given time series, in the presence of dependent and heteroscedastic errors. The identi_ability problem of the new model is studied; the notion of "instan-taneous frequency" is rigorously de_ned; the adaptivity and robustness properties of the Synchrosqueezing transform are theoretically justi_ed; and a series of simulation results are provided to demonstrate its numerical performance. We directly apply this method to analyze the incidence time series of varicella and herpes zoster in Taiwan. If time permits, I will provide another examples in sleep depth detection, anesthesia depth prediction and ventilator weaning prediction. - Tuesday, 22nd January, 2013
Title: Fake uniformity in tomographic shape inversion: A case study on the interplay of stochastic geometry and harmonic analysis Speaker: Dr. Christian RAU, School of Mathematical Sciences , Monash University, Australia Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: V. Panaretos (Ann. Stat., 2009) introduced an inverse problem of a tomographic nature, where an unknown three-dimensional probability density is projected into the plane after it has been subjected to a uniform (Haar distributed) rotation. He derived a shape inversion formula that applies to a 'discretisation' of this problem. In this talk, we replace the uniform rotation by a more general one satisfying a weaker symmetry property called conjugation-invariance, but on the other hand, treat the shape -- that is, a related Gram matrix -- as a known test function. We uncover and characterise a 'fake uniformity' property that describes the situation where, based on the expectation of the test function, a rotation distribution cannot be distinguished from the uniform one. This uses the theory of spherical harmonics in a way that appears to be significantly different from that of previous instances, described for example in the monograph of H. Groemer (1996). - Monday, 28th January, 2013
Title: An Adaptive Energy Stable Semi-Implicit Spectral Deferred Correction Methods for Phase-field Models Speaker: Mr. YANG Jiang, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 14:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We construct a high order energy stable scheme to simulate three phase-field models including Allen-Cahn equations, Cahn-Hilliard equations and thin film models, which achieves by combining semi-implicit spectral deferred correction (SISDC) cite{M.L. MINION} methods and energy convex splitting cite{D. EYRE}. We first get prediction values for the correction step via an energy convex splitting scheme. This scheme is a linear unconditionally stable one-step method but it is only first-order accurate. The SISDC is used to get higher order accuracy. As this scheme is linear, what we need to solve during every loop of SISDC is only involved the Laplace operator. Straightforwardly, we will utilize a fast solver to enhance the computing effectiveness and save the storage. To overcome the numerical instability caused by the correction steps and, meanwhile, to enhance the efficiency an adaptive strategy is proposed to simulate the dynamical evolution correctly. Numerical experiments are presented to demonstrate high order accuracy and efficiency of SISDC to solve these three models.