Registered Data

[CT110]

[02444] Pricing American XVA with stochastic default intensity

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We derive a PDE model for American derivatives' pricing including the valuation adjustment (XVA), assuming mean-reverting default risk for the counterparty, and constant default risk for the self-party. There are two nonlinear source terms, one from the American constraint and one from the XVA, handled by a double-penalty iteration. We also derive asymptotic approximations to the XVA price and to the free boundary. We present numerical experiments to study the accuracy and effectiveness of the 2D PDE and asymptotic approximations.
  • Classification : 65Mxx, 65Nxx, 91Gxx
  • Author(s) :
    • Christina Christara (University of Toronto)
    • Yuwei Chen (University of Toronto)

[02510] A posteriori virtual element method for the acoustic vibration problem

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : In two dimensions, we propose and analyze an a posteriori error estimator for the acoustic spectral problem based on the virtual element method in H(div,Ω). Introducing an auxiliary unknown, we use the fact that the primal formulation of the acoustic problem is equivalent to a mixed formulation, in order to prove a superconvergence result, necessary to despise high order terms. Under the virtual element approach, we prove that our local indicator is reliable and globally efficient in the L2-norm. We provide numerical results to assess the performance of the proposed error estimator.
  • Classification : 65Mxx, 65Nxx, 65N25, 65N12
  • Author(s) :
    • Felipe Lepe (Universidad del Bío Bío)
    • David Mora (Universidad del Bío Bío)
    • Gonzalo Rivera (Universidad de Los Lagos)
    • Iván Velásquez (Universidad del Sinú Elías Bechara Zainúm)

[00365] Advancing Computerized Tomography: Deep-Learning based Regularization in Diffuse Optical Tomography

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : X-rays Computed Tomography is a main pillar of medical imaging which at present is experiencing a strong innovation phase. While new tomographic systems try to minimize X-rays exposure, non-trivial challenges exist, mainly increased noise levels and the need for dealing with low and high contrast regions. In this talk we will refer about our research on new algorithms able to efficiently deal with this trade–off, with specific reference to Diffuse Optical Tomography.
  • Classification : 65Z05, 65N20, 65N80, 68T07
  • Author(s) :
    • Paola Causin (University of Milano )
    • Andrea Aspri (University of Milano )

[00651] Parallel Coordinate Descent Methods for Full Configuration Interaction

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Solving the time-independent Schrödinger equation gives us full access to the chemical properties of molecules. Among all the ab-initio methods, full configuration interaction (FCI) provides the numerically exact solution under a predefined basis set. However, the FCI problem scales factorially with respect to the number of bases and electrons and suffers from the curse of dimensionality. The FCI problem could be reformulated as an unconstraint minimization problem. This work proposes a novel algorithm to address the minimization problem. The algorithm introduces an extra search dimension to enable the exact linesearch for the multi-coordinate descent method, which could be fully parallelized. Hence, the proposed algorithm benefits from both exact linesearch and parallelization. Numerically, we demonstrate the parallel efficiency of the algorithm. The algorithm achieves better energy and parallelism on systems with approximately a hundred electrons than other existing methods.
  • Classification : 65Z05, 68Q12
  • Author(s) :
    • Yuejia Zhang (Fudan University)
    • Yingzhou Li (Fudan University)

[01414] Solving multidimensional elliptic problems in unbounded domains using quasi-rational functions

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : The recent discovery of a family of multidimensional functions ([1,2]) has led to the design of an efficient numerical method for solving elliptical problems in unbounded domains, without truncation. In this talk we present the method, the proof of its convergence and some highly promising numerical results. Applications of the method are numerous and are currently being explored. Ref.: 1. Arar and Boulmezaoud, J. Math. Anal. Appl. 400 (2013). 2. Boulmezaoud and al., M2AN 50 (2016).
  • Classification : 65Z05, 35J15, 35C10, 35C20
  • Author(s) :
    • Tahar Zamene BOULMEZAOUD (University of Versailles SQY and University of Paris-Saclay)