Fyodor Dostoevsky (1821-1881) in |

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.