Hedging diffusion processes by local risk minimization with applications to index tracking

This paper extends the local risk-minimization criterion for hedging contingent claims, as introduced in Föllmer 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], Föllmer 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.