Abstract:
This paper extends the local risk-minimization criterion for hedging contingent claims, as
introduced in Follmer and Sondermann [Hedging of non-redundant contingent claims.
In: Hildenbrand, W., Mas-Colell, A. (Eds.), Contributions to Mathematical Economics. Elsevier
Science, North-Holland, Amsterdam, pp. 205–223], Follmer and Schweizer [Hedging of contigent
claims under incomplete information. In: Davis, M., Elliot, R. (Eds.), Applied Stochastic Analysis,
Stochastic Monographs, vol. 5, Gordon and Breach, London/New York, pp. 389–414] and
Schweizer [Option hedging for semimartingales. Stochastic Processes and their Applications 37,
339–363], to the hedging of entire stochastic processes, and determines the necessary and sufficient
conditions under which this is possible. The results are then applied to the problem of stock index
tracking to obtain simple criteria for selecting the optimal set of assets with which to form tracker
portfolios, and to derive a value-at-risk type measure for the set of assets used.
