Properties of option prices, stochastic time and convexity of 
solutions to parabolic equations

We study properties of prices of European options on one
or several underlying assets. In particular, we are interested in 
questions concerning the convexity of the price in the underlying
asset. The issue of convexity is, for instance, important in hedging.
These questions lead us to study the convexity of solutions to parabolic
equations with convex initial conditions. It turns out that our methods
as well as the results are quite different in the case of one underlying
asset (one spatial variable) and several underlying assets (several
spatial variables), respectively. This is joint work with Svante Janson.