2022年度

Math-Fi seminar on 21 Apr.

2022.04.20 Wed up
  • Date: 21 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 17:00-18:00
  • Speaker:  Jiro Akahori (Ritsumeikan University)
  • Title:  Variational approach to optimal stopping problems revisited
  • Abstract: 
After reviewing besoussan-lions’s variational approach, I will discuss its applications to numerical problems; discretization error, deep solver, and so on.  The talk will be in English.

Math-Fi seminar on 14 Apr.

2022.04.14 Thu up
  • Date: 14 Apr. (Thu.)
  • Place: On the Web
  • Time: 17:00-18:30
  • Speaker:  Umut Cetin (London School of Economics)
  • Title:  Speeding up the Euler scheme for killed diffusions
  • Abstract:
Let X be a linear diffusion taking values in  (l,r) and consider the standard Euler discretisation to compute the fair price of a Barrier option written on X that becomes worthless if X hits one of the barriers before the maturity date T. It is well-known since Gobet’s work that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to N^{-1/2} with N being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to 1/N, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.
 

Math-Fi seminar on 7 Apr.

2022.04.11 Mon up
  • Date: 7 Apr. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker:  Andrey Pilipenko (Ukraine National Academy of Sciences)
  • Title: Limit behavior of perturbed random walks
  • Abstract:
A particle moves randomly over the integer points of the real line. Jumps of the particle outside the membrane (a fixed “locally perturbating set”) are i.i.d., have zero mean and finite variance, whereas jumps of the particle from the membrane have other distributions with finite means which may be different for different points of the membrane; furthermore, these jumps are mutually independent and independent of the jumps outside the membrane. We prove that the weak scaling limit of the particle position is a skew Brownian motion.

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