Hedging contingent claims on semimartingales
The paper deals with the second fundamental theorem of asset pricing which establishes the equivalence of complete markets and the uniqueness of equivalent martingale probability measures. The authors consider the replication of cash flows under the true or statistical probability measure in an economy with infinitely many assets which may possess arbitrage opportunities. In this economy discounted asset prices are local martingales with respect to a signed and local martingale measure. The authors show that completeness is connected to the uniqueness of the signed equivalent local martingale measure. The results are illustrated by the Black-Scholes economy for a pure jump term structure model and by an economy trading a single stock and derivatives on this stock with stock driven by a Lévy process.
scientific article; zbMATH DE number 1336677