Pricing derivatives of American and game type in incomplete markets
type: Item
instance of: scholarly article
title: Pricing derivatives of American and game type in incomplete markets
zbMATH Open document ID: 1052.91039
author: Jan Kallsen
author: Christoph Kühn
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91A15
zbMATH DE Number: 2118699
zbMATH Keywords: American options
zbMATH Keywords: game contingent claims
zbMATH Keywords: neutral derivative pricing
zbMATH Keywords: Dynkin game
zbMATH Keywords: \(\sigma\)-supermartingale
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s00780-003-0110-7
OpenAlex ID: W2095499328
DOI: 10.1007/S00780-003-0110-7
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description: scientific article; zbMATH DE number 2118699