R. Vilela Mendes
The fractional volatility model: No-arbitrage, leverage and completeness.
Tue, 05/15/2012 - 15:01 — SomNambulAuthors: R. Vilela Mendes, M. J. Oliveira, A.M. Rodrigues
Subjects: Statistical Finance
AbstractBased on a criterion of mathematical simplicity and consistency with
empirical market data, a stochastic volatility model has been obtained with the
volatility process driven by fractional noise. Depending on whether the
stochasticity generators of log-price and volatility are independent or are the
same, two versions of the model are obtained with different leverage behavior.
Here, the no-arbitrage and completeness properties of the models are studied.Portfolios and the market geometry.
Tue, 08/23/2011 - 15:01 — SomNambulAuthors: R. Vilela Mendes, Samuel Eleutério, Tanya Araújo
Subjects: Portfolio Management
AbstractA geometric analysis of the time series of returns has been performed in the
past and it implied that the most of the systematic information of the market
is contained in a space of small dimension. Here we have explored subspaces of
this space to find out the relative performance of portfolios formed from the
companies that have the largest projections in each one of the subspaces. It
was found that the best performance portfolios are associated to some of the
small eigenvalue subspaces and not to the dominant directions in the distances
matrix.The fractional Poisson measure in infinite dimensions.
Thu, 02/11/2010 - 16:02 — SomNambulAuthors: Maria Joao Oliveira, Jose Luis da Silva, Habib Ouerdiane, R. Vilela Mendes
Subjects: Probability
AbstractThe Mittag-Leffler function $E_{\alpha}$ being a natural generalization of
the exponential function, an infinite-dimensional version of the fractional
Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)
:=E_{\alpha}(\int (e^{i\phi(x)}-1)d\mu (x)) \] which we prove to fulfill all
requirements of the Bochner-Minlos theorem.
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