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), Manuel Guerra, João Guerra, João Janela, Beatriz Leal, Sara Lopes, Carlos Oliveira, Telmo Peixe, Gilson Silva, Long Teng, Maria Valente
SummaryThe aim of this project 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 associated
to the fractional Black-Scholes model and clarification of absence of arbitrage in the resulting
The project will reinforced by the collaboration of a research team at Wuppertal University,
Germnay. Both teams will explore significant complementarities in cooperative research work, with
special emphasis on qualification of young academics in an international environment.

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