Abstract
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. We show that for this class of processes the optimal endowment and strategy can be expressed quite explicitly. The corresponding formulas involve Laplace- or Fourier-type representation of the contingent claim. As a by-product we solve a dynamic version of Markowitz' mean-variance portfolio optimization problem. A number of examples illustrates that our formulas are fast and easy to evaluate numerically. In the second part of the talk we discuss some recent extensions to a multivariate setting and multi-asset options, the problem of hedging with a surragate asset, and path-dependent options. The talk is based on joint work with L. Krawczyk and J. Kallsen
Contact person:Søren Asmussen.