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Event(s) on January 2007
- Tuesday, 16th January, 2007
Title: Pricing Participating Products Under a Generalized Jump-Diffusion with a Markov-switching Compensator Speaker: Dr. Ken Siu, Department of Actuarial Mathematics and Statistics, Heriot-Watt University, UK Time/Place: 14:30 - 15:30
Abstract: We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with Markov-switching compensator. We suppose that the jump component is specified by the class of Markov- modulated kernel-biased completely random measures, which provides a great deal of flexibility in modeling different types of finite and infinite jump activities. We also provide additional flexibility to incorporate the impact of structural changes in macro-economic conditions and business cycles on the valuation of participating policies by introducing a continuous-time hidden Markov chain. In particular, we assume that the market interest rates, the drift, the volatility and the compensator of the reference asset switch over time according to the state of the hidden Markov chain. We employ the Esscher transform to determine an equivalent martingale measure under the incomplete market setting. We shall conduct simulation experiments to compare the fair values of participating products implied by our model with those obtained from other existing models in the literature and highlight some features that can be obtained from our model.
- Thursday, 18th January, 2007
Title: Probabilistic Method and Coloring of Graphs Speaker: Mr. L. Bian, Institute of Applied Mathematics, Lanzhou Jiaotong University, China Time/Place: 14:30 - 15:30
Abstract: Probabilistic method has been proved to a useful tool for showing some properties and existence of certain graphs. Since P. Erdős (1974) first adopted probabilistic method to show that the Ramsy number r(k, k) 2 ^(k/2), similar method has been applied to graphical parameter estimation. It is noteworthy that Lovász Local Lemma became an important tool in probabilistic method. In this presentation, we show how to use Markov inequality and Lovász Local Lemma to obtain the upper bounds of (i) the adjacent vertex-distinguishing edge chromatic number; (ii) the acyclic edge chromatic number; and (iii) the adjacent vertex-distinguishing acyclic edge chromatic number, of a graph.
- Tuesday, 23rd January, 2007
Title: Parabolic Variational Inequalities: The Lagrange Multiplier Approach and Applications to Mathematical Finance Speaker: Prof. Kazufumi Ito, Department of Mathematics, North Carolina State University, USA Time/Place: 11:30 - 12:30
Abstract: Parabolic variational inequality are discussed and existence and uniqueness of strong as well as weak solution is established. Our approach is based on a Lagrange multiplier treatment and existence is obtained as the unique asymptotic limit of solutions to a family of appropriately regularized nonlinear parabolic equations as the regularization parameter tends to infinity. Monotonicity results of the regularized solutions and convergence rate estimate are established. The results are applied to the Black-Scholes model for American options. The case of the bilateral constraints is also treated. Numerical results for the Black-Scholes model are presented and demonstrate the practical efficiency of our results.
- Wednesday, 31st January, 2007
Title: Centre for Mathematical Imaging and Vision (CMIV) Lecture Series Lecture 1: Defining a Data Fidelity Term by a Polytope: Application to Image Restoration and Compression Speaker: Prof. Francois Malgouyres, Laboratoire Analyse, Géométrie et Applications, Universiti Paris 13, France Time/Place: 14:00 - 15:00
- Wednesday, 31st January, 2007
Title: Continuous Methods in Optimization Speaker: Mr. Leihong Zhang, Department of Mathematics, Hong Kong Baptist University, HKSAR, China Time/Place: 15:30 - 16:30
Abstract: Continuous method (or trajectory method) is a new topic in optimization. It involves basically the design of some suitable differential equations and of some special efficient integration schemes. In this prospect, we provide a Newton-type method for unconstrained optimization and a modified projective dynamic for minimizing some concave optimization problems resulted from extreme and interior eigenvalue problems. The Newton-type method is shown that for a general function f(x), it converges globally to a connected subset of the stationary points of f(x) under some mild conditions; and converges globally to a single stationary point for a real analytic function. The method reduces to the exact continuous Newton method if the Hessian matrix of f(x) is positive definite. The convergence of the new method on 18 standard test problems in the literature are also reported. For our modified projective dynamic, we prove that it possesses not only the convergence properties similar to the old one, but also some other nice features. The efficiency of this modification is both addressed in theory and verified in numerical testing. Some further and promising work is also discussed.