Research projects

Project CEMAPRE internal

TitleFRACTAL FRActional models and ComputaTionAL finance - Modelos fracionários e finanças computacionais
ParticipantsJosé Cruz, Matthias Ehrhardt, Francisco Fonseca, José Pedro Gaivão, Maria do Rosário Grossinho (Principal Investigator), João Guerra, Manuel Guerra, João Janela, Beatriz M Leal, Sara Lopes, Carlos Oliveira, Telmo Peixe, Daniel Sevcovic, Gilson Silva, Long Teng, Maria Valente
SummaryThis project is basically the continuation of the previous project submitted for 2019 and will now
count also with Daniel Sevcovic (Univ Bratislava).
As referred, its aim is to develop analytical and numerical studies for boundary value problems
for fractional partial differential equations (fPDEs), and to focus on possible applications.
Suggested by the recent literature for the application of fPDEs in finance (e.g. in option pricing
models based on Lévy processes or fractional Brownian motion), we are concerned with:
o analytical study of fPDEs (existence and uniqueness results; properties of the solution)
o numerical results and computational implementation
o applications to financial option pricing, including the rigorous derivation of the fPDE
to the fractional Black-Scholes model and clarification of absence of arbitrage in the resulting
The project will continue to reinforce the collaboration of a research team at Wuppertal
Germany. progressing in the work developed in 2019 with special emphasis on qualification of young
academics in an international environment, Special support will be given to the PhD student Beatriz
Malheiros Leal.
Nonlinear Models on Computational Finance are generically our main concern.

Keywords: Fractional Brownian motion; Fractional differential equations; Nonlinear models;
Computational finance