Research projects

Project CEMAPRE internal

TitleStochastic and computational finance
ParticipantsNicola Cantarutti, Nuno Miguel Conceição, José Cruz, Fernando Gonçalves, Maria do Rosário Grossinho (Principal Investigator), João Guerra, Manuel Guerra, João Janela, Yaser Kord, Sara Lopes, Pedro Pólvora, Gilson Silva
SummaryWe aim to work on nonlinear generalization of the Black-Scholes equation for pricing financial
instruments. The relevance of this subject relies on the fact that lhe classic Black-Scholes model
has been established under some restrictive assumptions like e.g., frictionless, liquid and complete
markets, etc. These assumptions do not hold in pratice which points out some drawbacks of the

Addressing these issues leads us to the study of some mathematical problems that concern nonlinear
PDEs or PIDEs. So, we will consider
- nonlinear PDEs
- nonlinear PIDEs
- discretization and numerical analysis

We will study the problem of existence of weak, or/ and viscosity solutions for parabolic PDEs and
PIDEs related to the option pricing problem in financial models based on Gaussian or exponential
Lévy processes, and the efficiency of numerical schemes for solving such PDEs and PIDEs.