Pricing derivatives of American and game type in incomplete markets
The paper shows that the concept of neutral derivative pricing can be adapted quite naturally to American options on incomplete markets. It is demonstrated that the neutral price of an American option coincides, as in complete case, with the supremum of the neutral prices of all implied European claims. American options are treated in this paper as special cases of game contingent claims. The latter naturally generalizes American contingent claims by giving both counterparties the right to cancel the contract prematurely. This generalization requires some mathematical, but no additional conceptual efforts. On the technical level, an important role is played by \(\sigma\)-sub- and \(\sigma\)-supermartingales. Their characterization in terms of semimartingale characteristics is presented.
scientific article; zbMATH DE number 2118699