Projects

Here you can find the abstracts of my bachelor and my master thesis. Full versions are available upon request.

  • Bachelor thesis “Stochastic optimal control: Strategies for illiquid financial markets”.
  • Master thesis “Statistical inference for stochastic partial differential equations: Localized estimation of the diffusivity and the source”.

I am also interested in the numerical simulations of semilinear SPDEs in order to visualize their (statistical) properties. Soon, I will post the Julia Code that implements the semi-implicit Euler-Maruyama scheme from the very nice book “An Introduction to Computational Stochastic PDEs” by Catherine E. Powell, Gabriel J. Lord, and Tony Shardlow (Cambridge University Press, 2014) for the SPDE

\[\operatorname{d}X_t = (AX_t + F(X_t))\, \operatorname{d}t + \operatorname{d}W_t, \quad (Az)(x) = \frac{\operatorname{d}}{\operatorname{d}x}\left(\vartheta(x)\frac{\operatorname{d}}{\operatorname{d}x}z(x)\right) + a(x)\frac{\operatorname{d}}{\operatorname{d}x}z(x)\]

on the (spatial) domain \((0,1)\) with Dirichlet boundary conditions with space-time white noise \(\operatorname{d} W_t\).


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