The Fourth Bachelier Colloquium on Mathematical Finance and
Stochastic Calculus
                                                           January 24-31, 2010

         Scientific Program

         Main Topic: Mathematical Models of Financial Markets
with Transaction Costs and Optimal Control

Theory of financial markets with transaction costs still
remains the cutting edge of the current development in
mathematical finance. It aims to take into account
market imperfections, always existing in the real world.
During the initial stage, the problems related with
market friction was considered as extremely difficult.
Nowadays, due to efforts of several research group,
the theory is put on a firm mathematical foundation.
Stimulated by its practical importance, it is quickly
growing field involving new and new problems
requiring fresh mathematical ideas.
These ideas come from various branches: stochastic
calculus, geometric functional analysis, theory of viscosity
solutions for non-local PDEs, convex geometry, stochastic
optimization, theory of economic equilibrium.
Recently, an essential progress was achieved in the
consumption--investment problem in models where the prices
may have jumps. Nevertheless, the complete solution is still
a mathematical challenge. This is the reason why we consider
it as the main topic of the 4th Bachelier colloquium.