Preliminary list of abstracts

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Sparse Grids and Multi-Level Monte Carlo
Keywords: Sparse Grids; Multi-Level Monte Carlo; Computational Finance
Wed, 11:10--11:35
  • Gerstner, Thomas (Institut für Mathematik, Universität Frankfurt, Germany)

The Multilevel Monte Carlo method introduced by Michael Giles is a technique to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In this method, path simulations with different timesteps are combined in such a way that the ratio of computational cost and error (variance) is minimized. This can reduce the complexity, up to a logarithmic factor, by one order of magnitude. It has many applications, particularly in computational finance.

In this talk, we will show that the Multilevel Monte Carlo method can be interpreted as a sparse grid method in dimension-samples space. We extend the method to deal with adaptivity and apply this adaptive Multilevel Monte Carlo method to the pricing of special financial products such as barrier options.