Colloquium/Seminar

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Event(s) on April 2012


  • Tuesday, 10th April, 2012

    Title: An Introduction To Mathematical Finance From An Applied Mathematics Perspective
    Speaker: Prof. Peter W. Duck, School of Mathematics, The University of Manchester, UK
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The seminal work of Black & Scholes (1973) and Merton (1973) has led to an explosion of ideas in the theory of the pricing of financial derivatives, in particular options (and a joint Nobel price for economics). A put (call) option is a contract between two parties, in which one party, the holder, has the right to sell (buy) an asset from the other party, the writer. Obviously the right implies some value to this contract, and this is what option pricing theory is all about. In this talk a brief overview of the subject is given, Monte-Carlo simulation methods are described, and a short derivation of the now well known Black-Scholes equation is presented. This equation, which is pivotal in numerous studies of this kind is of backwards parabolic type, although a series of routine transformations can reduce the basic form to the heat-conduction equation. The first case considered is that of European options (which can only be exercised on a prescribed date), for which exact solutions exist. The second case considered is that of American options. This class of option is one where the holder of the option has the right to exercise at any time during the lifetime of the option. These lead to free boundary problems (basically the location in asset space where the option should be exercised), and as such these are nonlinear problems. Nonetheless, these are amenable to standard computational techniques. No prior knowledge of Mathematical Finance will be assumed!


  • Tuesday, 17th April, 2012

    Title: Asymptotic Analysis of Orthogonal Polynomials via Three-Term Recurrence Relations
    Speaker: Dr. Yutian Li, Department of Mathematics, City University of Hong Kong, Hong Kong
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Cheun Library, Ho Sin Hang Campus, Hong Kong Baptist University
    Abstract: Orthogonal polynomials play an important role in many branches of mathematical physics, for instance, quantum mechanics, scattering theory and statistical mechanics. A major topic in orthogonal polynomials is the study of their asymptotic behaviour as the degree grows to infinity. One important property of orthogonal polynomials is that they all satisfy a three-term recurrence relation. In this talk, we shall present a summary of methods now available, which are based on recurrence relations and can be used to derive asymptotic approximations for orthogonal polynomials, not only when the variable is fixed but also when it is allowed to vary in an interval containing a transition point.


  • Tuesday, 24th April, 2012

    Title: DLS: Biological Network Inference From Genomics Data
    Speaker: Prof. Hongyu Zhao, Yale School of Public Health, USA
    Time/Place: 11:00  -  12:00 (Preceded by Reception at 10:30am)
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Revealing networks of biological components is one of the key questions in systems biology, and it has potential applications in understanding disease physiology and drug discovery in the area of network medicine. With advances in high throughput biology, we can now measure the expression levels and DNA variations at the genome level, either through microarrays or next generation sequencing. These data offer the opportunity to statistically infer genetic networks from these data. In this presentation, we discuss several approaches for network inference through jointly analyzing gene expression data under diverse conditions in combination of DNA variation data. We provide both theoretical and simulation results to investigate the properties of our procedures. We also demonstrate the usefulness of our approaches through their applications to real data. This is joint work with Hyonho Chun, Bing Li, Ruiyan Luo, Haisu Ma, and Xianghua Zhang.


  • Monday, 30th April, 2012

    Title: CMIV DLS: Chaotic Regularization
    Speaker: Prof. U. Ascher, University of British Columbia, Canada
    Time/Place: 16:30  -  17:30 (Preceded by Reception at 16:00pm)
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. Yet other, much faster gradient descent methods using bolder step size selection exist. They can be preferable to conjugate gradients when matrix-vector multiplications are performed inaccurately. These faster gradient descent methods, however, yield chaotic dynamical systems for the iteration residuals.
    The steepest descent method is also known for the regularizing or smoothing effect that the first few steps have for certain inverse problems, amounting to a finite time regularization. We further investigate using the faster gradient descent variants for this purpose in the context of denoising and deblurring of images and also of problems involving data inversion for elliptic PDEs. When the combination of regularization and accuracy requirements demands more than about a dozen steepest descent steps, the alternatives offer an advantage, even though (indeed because) the absolute stability limit of forward Euler is carefully yet severely violated.