We consider option pricing problems modeled by PDEs of Black-Scholes type. The PDE is discretized using finite differences in space and time. For high-dimensional problems the number of unknowns grows exponentially in the number of underlying assets (=dimensions) which is referred to as the "curse of dimensionality". To mitigate this curse we employ adaptivity in both space and time in order to place the grid-points in an optimal way. Here you find information on what we have accomplished so far.

The goal of the PhD-project is to extend the models to include also stochastic volatility and jumps in the underlying asset. Furthermore we intend to introduce adaptive high-order discontinuous Galerkin as time-discretization.

For more information, contact Lina von Sydow