Numerical Methods for Nonlinear PDEs in Finance

PhD defense: Sima Mashayekhi

Nonlinear Black-Scholes equations arise from considering parameters such as feedbackand illiquid markets effects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some finite difference schemes have been investigated to solve numerically such nonlinear equations.

However the analytical solution of the linear Black-Scholes equation is known, different numerical methods have been considered for solving the equation to make a general numerical scheme for solving other more complicated models with no analytical solutions such as nonlinear Black-Scholes models. Therefore at first some investigations for the standard linear Black-Scholes equation have been considered for instance choosing a suitable right boundary condition and applying some remedies for dealing with nonsmooth conditions of the equation. After that a number of nonlinear Black-Scholes models are reviewed and different numerical methods have been investigated for solving some of those models. At the end the numerical schemes have been compared with respect to order of convergence.

Supervisor: Ass Prof. Jens Hugger, Math, University of Copenhagen,

Co-supervisor: Prof. Rolf Poulsen, Math, University of Copenhagen,

Assessment committee:

Ass. Prof. Trine Boomsma (chairman), MATH, University of Copenhagen, Denmark

Senior Lecturer,  Lina von Sydow, Uppsala University

Ass. Prof. David Skovmand, Copenhagen Business School