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Event(s) on July 2017

  • Monday, 3rd July, 2017

    Title: Asymptotical Analysis of the Boltzmann equation: from cutoff to non-cutoff
    Speaker: Prof. HE Lingbing, Department of Mathematical Sciences, Tsinghua University, Beijing, China
    Time/Place: 14:00  -  15:00
    FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We investigate the asymptotics of the Boltzmann equation from the short-range interactions to long-range interactions. We prove the global well-posedness and give the precise description on the dynamics of the equations in a unified framework in the close-to-equilibrium setting. This is a joint work with Yulong Zhou.

  • Monday, 10th July, 2017

    Title: Smoothing spline mixed-effects density models for clustered data
    Speaker: Prof. WANG Yuedong, Department of Statistics & Applied Probability, University of California , Santa Barbara, U.S.A
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Smoothing spline mixed-effects density models are proposed for the nonparametric estimation of density and conditional density functions with clustered data. The random effects in a density model introduce within-cluster correlation and allow us to borrow strength across clusters by shrinking cluster specific density function to the population average, where the amount of shrinkage is decided automatically by data. Estimation is carried out using the penalized likelihood and computed using a Markov chain Monte Carlo stochastic approximation algorithm. We apply our methods to investigate evolution of hemoglobin density functions over time in response to guideline changes on anemia management for dialysis patients.

  • Thursday, 13th July, 2017

    Title: Bank monitoring incentives under moral hazard and adverse selection
    Speaker: Dr. ZHOU Chao, Department of Mathematics / Centre for Quantitative Finance, Faculty of Science, National University of Singapore, Singapore
    Time/Place: 17:30  -  18:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this paper, we extend the optimal securitization model of Possamaï and Pagès between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitanić, Wan and Yang, we characterize explicitly and rigorously the so-called credible set of the continuation and temptation values of the banks, and obtain the value function of the investor as well as the optimal contracts through a recursive system of first-order variational inequalities with gradient constraints. We provide a detailed discussion of the properties of the optimal menu of contracts. This is a joint work with Nicolás Hernández Santibáñez and Dylan Possamaï.

  • Tuesday, 25th July, 2017

    Title: Verifiable Metric Subregularity for Structured Convex Optimization Problems
    Speaker: Mr. Zeng Shangzhi, Department of Mathematics, Hong Kong Baptist University , HKSAR
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We consider a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a general closed proper convex function. We introduce the concept of metric subregularity, which is fundamental in the variational analysis area, to this study. It has been shown that the metric subregularity condition suffices to ensure the linear convergence rates of a host of first-order methods for solving convex optimization problems. We show that such a metric subregularity condition is mathematically favorable in the sense that some checkable assumptions on the objective function per se can be immediately discerned for guaranteeing the metric subregularity. It is notable that the literature of linear convergence analysis for various first-order methods in the convex programming context is dominated by error bound conditions which are generally not checkable. Our study is valid for a number of important applications. This study from the metric subregularity perspective opens the avenue of using some advanced variational analysis tools recently introduced for investigating the linear convergence rates of some popular first-order algorithms in convex optimization.



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