Monte Carlo Methoden II

Andreas Neuenkirch

2+2 SWS / 6 ECTS, M.Sc.

In dieser Veranstaltung werden wir u.a. folgende weiterführende Themen der stochastischen Numerik behandeln:

  1. Quantisierung
  2. Monte Carlo Verfahren für lineare Gleichungssysteme
  3. Numerische dynamische Programmierung

Termine etc.

  • Erste Vorlesung: Donnerstag, 13.02.2025,12:00 -- 13:45,  C 014 Hörsaal (A 5, 6 Bauteil C)
  • Erste Übung (vorläufiger Termin): Mittwoch, 19.02.2025, 08:30 -- 10:00, C 014 Hörsaal (A 5, 6 Bauteil C)
  • Prüfungszulassung: 50 % der Abgabenaufgabenpunkte; Zweierabgabe möglich
  • Termine für die mündlichen Prüfungen werden noch bekanntgegeben

Literatur

  • Lloyd, S.P. (1982) Least Squares Quantization in PCM. IEEE Transactions on Information Theory, 28, 129–137.
  • Foundations of Quantization for Probability Distributions, Lecture Notes in Mathematics, Siegfried Graf, Harald Luschgy, Springer, 2007
  • Numerical Probability, An Introduction with Applications to Finance, Gilles Pagès, Springer. 2018
  • J. Kieffer, Exponential rate of convergence for Lloyd's method I, in IEEE Transactions on Information Theory, vol. 28, no. 2, pp. 205–210, March 1982
  • George Forsythe, Richard Leibler, Matrix inversion by a Monte Carlo method, Math. Tables and Other Aids to Computation, 4 (1950), 127–129
  • W. Wasow, A note on the inversion of matrices by random walks, Math. Tables and Other Aids to Computation, 6 (1952), 78–81
  • J. Curtiss, A theoretical comparison of the efficiencies of two classical methods and a Monte Carlo method for computing one component of the solution of a set of linear algebraic equations, John Wiley and Sons, Inc., New York, 1956, 191–233
  • Introduction to Probability. Charles M. Grinstead and J. Laurie Snell, American Mathematical Society; 2nd Revised edition (July 1, 1997)
  • Thomas Müller-Gronbach, Erich Novak, Klaus Ritter, Monte Carlo-Algorithmen, Springer Berlin, Heidelberg 2012
  • J. N. Tsitsiklis and B. Van Roy, Regression methods for pricing complex American-style options, IEEE Transactions on Neural Networks, vol. 12, no. 4, pp. 694–703, July 2001
  • Lars Stentoft, Convergence of the Least Squares Monte Carlo Approach to American Option Valuation, Management Science, Vol. 50, No. 9 (Sep., 2004), pp. 1193-1203