Pricing derivatives of American and game type in incomplete markets

In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively. On the technical level, an important role is played by <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\sigma$</EquationSource> </InlineEquation>-sub- and <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\sigma$</EquationSource> </InlineEquation>-supermartingales. We characterize these processes in terms of semimartingale characteristics. Copyright Springer-Verlag Berlin/Heidelberg 2004