Numerical analysis of nonlinear PDEs in option pricing: finite difference and splitting methods.
7 December 2016
UAntwerpen, Campus Middelheim, A.143 - Middelheimlaan 1 - 2020 Antwerpen (route: UAntwerpen, Campus Middelheim
Organization / co-organization:
Department of Mathematics & Computer Science
Karel in 't Hout & Tatiana Chernogorova
PhD defence Radoslav Valkov - Faculty of Science, Department of Mathematics & Computer Science
In this thesis, we consider numerical techniques for two fundamental nonlinear Black-Scholes models. The first one governs the American option valuation and is described by a partial differential inequality. The second model is given by the so-called Black-Scholes Barenblatt PDV, which takes into account the uncertainty in the volatility prediction.
We present different results with respect to each of these problems. The emphasis is on models that are highly non-trivial. Although this is a very challenging task, this thesis is a novel contribution to the contemporary literature for numerical methods for nonlinear financial models.