Project CEMAPRE internal
|Title||Stochastic and computational finance|
|Participants||Nicola Cantarutti, Nuno Miguel Conceição, José Cruz, Fernando Gonçalves, Maria do Rosário Grossinho (Principal Investigator), Manuel Guerra, João Guerra, João Janela, Yaser Kord, Sara Lopes, Pedro Pólvora, Gilson Silva, Onofre Simões|
|Summary||We aim to address two main topics of mathematical finance concerning nonlinear generalizations of|
the Black-Scholes (BS) equation. Nonlinear models can capture several important phenomena like
transaction costs, investor's risk from unprotected portfolio, investor's expected utility
maximization, illiquid markets, large traders feedback influence. So, we are concernd with:
- perpetual put options in which the volatility function depends on the second derivative of the
option price itself.
- financial models based on jump processes.
We also want to focus on rigorous and advanced quantitative methods for the pricing and hedging of
counterparty credit and funding risk.
Addressing these issues leads us to the study of some mathematical problems that concern nonlinear
PDEs, PIDEs, free boundary problems, numerical analysis and simulation.