Research

(...) I have always been ridiculous, and
I have known it, perhaps, from the hour I was born. Perhaps
from the time I was seven years old I knew I was ridiculous.
Afterwards I went to school, studied at the university, and, do
you know, the more I learned, the more thoroughly I
understood that I was ridiculous. So that it seemed in the end
as though all the sciences I studied at the university existed
only to prove and make evident to me as I went more deeply
into them that I was ridiculous. (...)

Fyodor Dostoevsky (1821-1881) in The Dream of a Ridiculous Man.

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My current reseach activity is focused on Financial Mathematics - the use of modern mathematical tools from stochastic analysis, probability theory and statistics to understand, model and make decisions in Financial Markets. As a member of PhiMac I am involved in a number of research projects in this area, such as pricing and hedging in incomplete markets (applications of utility--based pricing to, among others, real options, stochastic volatility and employee stock options), positive interest rates (using the chaotic framework introduced by Hughston and Rafailidis), systemic risk and stability (using network analysis and the tools from agent-based computational economics) and more recently asset price bubbles (trying to use the techniques from mathematical finance to formalize the ideas in the Minsky model).

The research page for PhiMac contains a short description of these projects, as well as whom I am collaborating with in each of them.

The subject of my PhD was Information Geometry, and I still have an active interest in the area. It is concerned with the furnishing of geometrical structures to families of probability distributions, both classical and quantum, either finite or infinite dimensional. A look at the recent conference held in Leipzig  should give a good perspective of the kind of problems and applications of the subject. I personally arrived at information geometry because it can provide a general way to develop dynamical models in nonequilibrium statistical mechanics, but now I'm naturally more interested in possible applications in mathematical finance.

Finally, back in my undergraduate times at the University of São Paulo, I developed a strong interest for History of Science, having written a couple of essays on History of Mathematics and presented several talks in conferences and meetings, both in Brazil and abroad. Although not working professional on such matters any more, I am still a member of the Sociedade Brasileira de História da Ciência and try to keep updated with the work of my historian friends, nurturing the desire to do research in the field some day in the future.