• Lydie Mpinganzima, presentation of MSc thesis, December 16, Dept. of Math., LiU

Title: Data Assimilation and Optimal Control with Differential Equations
Abstract: We study the problem of finding the best approximation of an unknown exact solution to differential equation from a set of available measurements. We define a nearest neighbour interpolant and formulate and solve a minimization problem. We also verify that the solution to the minimization problem is a better approximation than the interpolant both; theoretically and numerically. We finally apply these methods to a problem concerning coefficient identification.

  • Lydie Mpinganzima, PhD students' seminar, April 29, Dept. of Math., LiU

Title: A data assimilation approach to coefficient identification
Abstract: The thermal conductivity properties of a material can be determined experimentally by using temperature measurements taken at specified locations inside the material. We examine a situation where the properties of a (previously known) material changed locally. Mathematically we aim to find the coefficient k(x) in the stationary heat equation (kT_x)_x = 0; under the assumption that the function k(x) can be parametrized using only a few degrees of freedom.

  • Marcel Ndengo Rugengamanzi, PhD students' seminar, April 23, Dept. of Math., LiU

Title: An optimization framework for estimating forward rates
Abstract: The topic of this paper is the development of an optimization framework that can be used for estimating the forward rates. While we review some of the traditional techniques such as interpolation methods and some suitable smooth functions employed for that purpose, the current work suggests a constrained optimization model that proved to be rather general for estimating the forward rates and handle any interest rate instruments. The paper intends to show that all existing methods and smooth functions used to date are particular cases for the suggested ones. For computation purposes, we use an interior point based solver developed by Jörgen Blomvall. Preliminary results show that the proposed model guarantees smooth forward rate curves and prices interest rate instruments traded in the market realistically.

  • Marcel Ndengo Rugengamanzi, PhD students' seminar, March 11, Dept. of Math., LiU

Title: An optimization framework for estimating forward rates
Abstract: We have taken a sound interest in modelling of interest rate curves and have surveyed quite a number of existing models in which analysis approches are used to estimate the forward rate curves. The question that is yet to be explored fully is whether or not existing models, together with analytical approaches, produce realistic market prices, for all tradable securities. Estimation of the forward rates is as important as the methods used by either reasechers, investors or market makers. While keeping the validity of methods like interpolations, cubic splines approximation, and the likes, we also embark on estimation of the forward rates curves but propose a general optimization framework and show that all existing models for this purpose are special cases for this one. From early results, the proposed framework and the solution method that uses the 'Interior point method', suggests gain in getting reliable day to day smooth forward rate curves that indicates realistic estimation of the market prices.

  • Marcel Ndengo Rugengamanzi, meeting for PhD students from the Dept. of Math. at LiU and Umeå university, January 12, Dept. of Math., LiU


  • Marcel Ndengo Rugengamanzi, meeting for alumni from the Dept. of Math., September 12, Dept. of Math., LiU

Title: Optimized forward rates