BFS 2002 

Contributed Talk 
Tom Hurd, Tahir Choulli
This paper addresses Merton's portfolio optimization problem in the general setting of exponential Lévy stock model. We investigate three canonical examples of utility functions, exp(x),x^p/p,log x and in each case give the general solutions of both the primal and dual optimal problems. To study the dual problem directly, we introduce a generalized notion of Hellinger process such that the solution of the dual problem is that supermartingale which minimizes the Hellinger process at each instant in time. We are especially interested in when this solution is a martingale: we find it fails to be a martingale in cases when there is a no borrowing/shortselling constraint which becomes binding.
http://icarus.math.mcmaster.ca/tom/finmath.html